Trigonometry Lesson #7: More Problem Solving... 111
5. From the top of a cliff 110 m high, an observer sees two boats, one directly behind the
other, heading for shore. The angle of depression from the observer to the boat furthest
from the observer is 48° and the angle of depression to the nearest boat is 57°.
Calculate the distance between the boats, to the nearest metre.
Answers
The distance between the two boats is found as 21.60 m.
What is termed as the angle of depression?The angle of depression is defined as "an angle made between the horizontal line and also the line of sight whenever an observer looks downwards at an object." When we look down, it determines the shift in angle of our vision.For the given question,
Let the distance of ship c from the bottom of the cliff is 'a'.
Let the distance between both ships is 'b' m.
The height of the cliff is 110 m.
The angle of depression by both the ship with the top of the cliff is 48° and 57°.
Data from the figure shown,
Consider right triangle ABD,
tan 48° = AB/BD
tan 48° = 110/(a+b)
a + b = 110/tan 48°
a + b = 99.04 .......eq 1
Now in right triangle ACD,
tan 57° = 110/a
a = 110/tan 57°
a = 71.43 m
Put the value of in eq 1.
a + b = 99.04
b = 99.04 - 71.43
b = 21.60 m
Thus, the distance between the two boats is found as 21.60 m.
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Related Questions
4 3/20 as a simplified common fraction
Answers
Answer:[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Find the greatest possible error for each measurement. 1 1/4
Answers
Answer:
12 should be 1 as in 1 foot. 1' 1/4"
Step-by-step explanation:
In the similar triangles below, what is the length DF
24 cm
16 cm
12 cm
8 cm
Help ASAP
Answers
Length of DF is 24cm.
Define similarity.If one figure may be produced from the other by a single transformation, or by a series of transformations, such as translations, reflections, rotations, and/or dilations, then and only then are two figures said to be similar. When there is a similarity transformation, the transformed image has the same shape as the original. There will always be similar varieties of triangles, quadrilaterals, and polygons. For instance, squares and equilateral triangles are both similar shapes. We know the lengths of comparable sides are proportional if two polygons resemble one another.
Given,
Two triangles are similar,
DF = AC (3)
DF = 8(3)
DF = 24
Length of DF is 24cm.
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The ratio 2/5:1/4 has a unit rate of 8/5 true or false
Please help!!!
Answers
Answer:
true
Step-by-step explanation:
2/5 to 1/40.40 to 0.25 (convert decimal to fractions)40 to 25 (multiply 100 to both numbers to obtain whole numbers)8 to 5 (common factor of 5 cancel out, b/c a ratio can be written as a fraction)8/55 inches5 inches3 inches8 inches
Answers
The area of a triangle is given by the following formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the length of the base and h is the height of the triangle.
In this case, the length of the base equals 8 inches and the height of the triangle equals 3 inches, by replacing 8 for b and 3 for h, we get:
[tex]A=\frac{8\times3}{2}=\frac{24}{2}=12[/tex]Then, the area of this triangle equals 12 square inches.
Minh borrowed $30,000 from a bank for a car loan. if the length of the car loan is 7 years and the intrest rate is 18%, what is the total amount he owes the bank at the end of the loan.
Answers
Including interest on the principal the total loan amount is $67800
A loan occurs when one or more individuals, businesses, or other entities lend money to additional individuals, businesses, or other entities.
A loan is obtained, and the recipient, or borrower, is typically liable for both the principal borrowed as well as interest payments until the debt is repaid.The principle amount borrowed, the interest rate the lender is charging, and the due date for repayment are often disclosed in the promissory note used to demonstrate the obligation. The subject asset(s) are temporarily divided between the borrower and the lender when a loan is issued.Interest on the loan = 30000 × 0.18 × 7 = $37800
Total amount to be paid = $ 30000 + $ 37800 = $67800
Hence he owes a total of $67800 to the bank.
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What is 1.28×10 power negative 1 ×10 power negative 2
Answers
Answer:
0.00128
Step-by-step explanation:
1.28 x 10^-1 x 10^-2
1.28 x 0.1 x 0.01
1.28 x 0.1 x 0.01
0.00128
Evan's parents budget 15% of their monthly disposable income of $5,200 for clothes. They budget 25% of the 15% budget amount for Evan's clothing, Evan buys his ownclothes above the budgeted amount. Evan had the following estimated totals for the six-month period from March through August: clothes = $1,278; repairs and alterations =$75; and dry cleaning = $70. How much will Evan have to pay out of his own pocket?$253.00$250.25$245,50$241.75None of these choices are correct.
Answers
First find the 15% of $5,200 to know how money they spend on clothing.
(15*5,200)/ 100 = $780
They budget 25% of the 15% budget amount for Evan's clothing
(25*780)/100 = 195 for each month
195*6 = $1,170 for the six-month period
The estimated totals for the six-month period is
$1,278 + $75 +$70 = $1,423
Make the subtraction between the six month period and the estimated totals for the six-month period:
$1,170 - $1,423 =-253
$253.00 is the amount that Evan have to paoy out of his own pocket.
2. Amy was asked to find mABC in the picture. Her work is shown below.
The alternate interior angles are congruent when the lines
are paralled so
mLABC-3(27)-47
-81-47
-34°
30-47-n+7
-47
+47
3n-+54
-n-h
20-54
2
n=27
Explain Amy's mistake
A
(3n-47)
(n+7)
B
D
Show all work to find the correct mABC.
Answers
Amy's mistake was she took the angles as alternate interior angles, rather they form supplementary angles. The measure of both angles are 118 and 62.
What are alternate interior angles?The alternate interior angles theorem states that if a transversal connects two parallel lines, the alternate interior angles are identical in size. If we know the measure of the corresponding alternate interior angle, we may use this theorem to determine the measure of the alternate interior angle.
As per the given question,
both angles are not alternate interior angles,
rather both of the angles are supplementary angles.
This means that both form the sum of 180
⇒ 3n - 47 + n + 7 = 180
⇒ 4n - 40 = 180
⇒ 4n = 220
⇒ n = 55
∴ The measure of both angles will be 3n - 47 = 118 and n + 7 = 62
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I have been trying for a long time and I’m still stuck on it
Answers
Answer:
I'm not quite sure what you're trying to get but if you wanted it simplified the answer is 8^32 and if you needed to rewrite the expression the answer is 2^96
Answer:
[tex]8^{32}[/tex] They are looking for the exponent k = 32
Step-by-step explanation:
[tex](8^{8}) ^{^{4} }[/tex] this means that we have
[tex]8^{8}[/tex] four times
[tex]8^{8}[/tex] x [tex]8^{8}[/tex] x [tex]8^{8}[/tex] x [tex]8^{8}[/tex] Each one of these is 8 8's
(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)
How many 8s is that? 32.
The power or powers principal tells us that we can just multiply the exponents. (8 x 4) = 32
7
Select the correct answer.
The parent function f(x)=√x is transformed to g(x) = -2f(x). Which is the graph of g?
Answers
For the given set of functions, the correct graph is given below.
What is a graph, exactly?The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.
Bar graphs, circle graphs, and line graphs are the three most often used types of graphs. Different types of data can be displayed using different types of graphs.
Figure 1 illustrates a graph, which is a graphic that explicitly depicts data along two dimensions.
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i have 2 mins pleaseeee
Answers
Answer: 216.77
Step-by-step explanation:
if AB = 7x, CB = 5x + 8, and BD ⊥ AC, what is the length of CB?
Answers
Answer: 28
Step-by-step explanation:
Because BD ⊥ AC we can conclude that AB is equal to CB so we can set them equal to each other in an equation.
7x = 5x + 8
2x = 8
x = 4
Because X is 4 we can fill it into CB's expression.
5(4) + 8
20 + 8
28
Please help me!!
A model is built having a scale of 1:15,000. How high would a 48,800-ft mountain be in the model? Give your answer to the nearest tenth of an inch.
(A.) 585600 in.
(B.) 19.5 in.
(C.) 3.3 in.
(D.) 39.0 in.
Answers
According to the scale the model mountain would be 39.04 inches.
Scale factor is the ratio of an object's original scale to that of a new object that is a representation of it but in a variety of sizes (bigger or smaller).
For instance, by increasing each side by, say, 2, we can expand the size of a rectangle with sides of 2 cm and 4 cm. The second figure will mimic the first figure, but every dimension of the second rectangle will be double that of the first figure. In this instance, the scale factor will be indicated by the number 2.
We now that 48800 feet = 48800 × 12 inches = 585600 inches
Scale = 1:15,000
height of model = 585600 ÷ 15000 = 39.04 inches
Hence the length of the model is 39.04 inches.
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I need help will give brainlist
Answers
Answer:
area of Δ K = 160 units²
Step-by-step explanation:
given scale factor of sides a , then
scale factor of areas = a²
here scale factor = 4 so factor of areas = 4² = 16
area of Δ J = [tex]\frac{1}{2}[/tex] × 5 × 4 = 10 units² , then
area of Δ K = 16 × 10 = 160 units²
Can someone help me with this math
Answers
Answer:
110 is the answer
Step-by-step explanation:
I can't not just under 30 letters so I'm doing this so I can actually submit this so u can see this answer so dont mind this part right here
1. Two functions are shown below.
f(x) = 2x² += 5x -5
g(x) = -2x - 10
What is the y-value when f(x) = g(x)?
Answers
The factors of the given functions are ( x+ 1 ) and ( 2x + 5 )
Given : The two functions are f(x) = 2x² += 5x -5 and g(x) = -2x - 10
In questions like these where we have to equate the two functions. We first have to do the obvious step that is equate the two values and then after that we are supposed to bring the like terms to one side because this will make the calculation both easy and less time consuming .
So as mentioned above
f( x ) = g ( x )
2x² + 5x -5 = -2x - 10
Now bring the like variables together ;
2x² + 7x = -10 + 5
this implies the equation becomes
2x² + 7x = - 5
which can also be written as
2x² + 7x + 5 = 0
Now we can solve it further by splitting the middle term
and we will get:
2x² + 5x + 2x + 5 = 0
Taking out the common factors '
x( 2x + 5 ) + 1 ( 2x + 5) = 0
( x+ 1 ) ( 2x + 5 ) = 0
Thus the two factors are ( x+ 1 ) and ( 2x + 5 )
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.Solve the multistep equation using distributive property.
2 (3x - 5) = 4x + 2
Answers
2(3x - 5) = 4x + 2
Using distributive property, we can write the equation as:
2(3x) - 2(5) = 4x + 2
⇒ 6x - 10 = 4x + 2
⇒ 6x - 4x = 10 + 2
⇒ 2x = 12
⇒ x = 12/2
⇒ x = 6
The value of x is 6
What is Distributive property?This property states that multiplying the total of two or more addends by a number will produce the very same result as multiplying each addend by the number separately and then adding the results together. The distributive property is the distributive law of multiplication over operations on basic arithmetic, such as addition and subtraction.Among the axioms for rings and fields are the distributive laws, such as the ring of integers (like the field of rational numbers). In this situation, multiplication has a distributive advantage over addition, while addition does not. Boolean algebras much like the algebra of sets or the switching algebra are two instances of structures with two operations that are each distributive over the other.To learn more about Distributive Property, refer to:
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What are the solutions to this equation?
22²= -10x + 12
x = 1
x=3
x = -6
x = -2
x = 6
x = -3
Answers
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included.It also goes by the name quadratic equations.The quadratic equation has the general form ax2 + bx + c = 0.where a, b, and c are numerical coefficients and x is an unknown variable.
What are the solutions to this equation?
22²-10x+12x
=484= -10x+12x
484=2x
2x=484
x=484/2
x=242
−10x+12x=1×x
Add the words in
2x=1×x
Simplify\s2x=x
Add or take away on both sides
2x−x=0
Take the terms x=0 out.
Evaluate 1×x=3x
Add the terms x=3x together.
Add or take away on both sides
x−3x=0
Remove the terms 2x=0.
Divide both sides by 2x to get 20.
Simplify −2−2x=0
Simplify x=0
Evaluate\s3x=−6x
Add or take away on both sides
3x+6x=0
9x=0 plus terms
Split the sides.
99x=90
Simplify99x=0
Simplify x=0
Evaluate−6x=−2x
Both sides should be added together, 6x+2x=0.
the expressions "4x=0"
Split the sides.
−4−4x=−40
Simplify−4−4x=0
Simplify x=0
Evaluate−2x=6x
2x6x=0 adds or subtracts both sides.
Remove the terms 8x=0.
Divide both sides by 8 to get 80.
Simplify−8−8x=0
Simplify x=0
Evaluates 6x=−3
Split the sides.
66x=6−3
Simplify 66x=−21
Simplify x=−21\s⎧x=242x=0x=0x=0x=0x=0x=−21
Simplify
⎧x=242x=0x=−21
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The results from a survey about the number of siblings a group of people have are shown in the table below. What is the median number of siblings? Number of siblings
Answers
Answer: The median number of siblings is 3.
Step-by-step explanation:
Put all of the numbers in STAT, Edit on your TI-84 Graphing Calculator.
Press STAT again and then slide over to CALC and hit 1-Var Stats.
Press ENTER and then 2ND, 2 for the FreqList, hit enter twice.
Scroll down to Med.
The median should equal 3.
The number of cases of a new disease can be modeled by the quadratic regression equation y = -2x^2 + 36x + 6, where x represents the year.
Which is the best prediction for the number of new cases in year 15?
Answers
Answer:
A hope it helps follow please
Step-by-step explanation:
hope you have a great day today
Find the missing side of the triangle.A. 19−−√ miB. 22–√ miC. 11−−√ miD. 1 mi
Answers
From the right angled triangle given,
To find the missing side, x, of the triangle, Pythagorean theorem is applied
The Pythagorean theorem formula is
[tex]\begin{gathered} (\text{Hyp)}^2=(\text{Opp)}^2+(\text{Adj)}^2 \\ \text{Hyp is the hypotenuse} \\ \text{Opp is the opposite } \\ \text{Adj is the adjacent} \end{gathered}[/tex]The dimensions of the triangle are
[tex]\begin{gathered} \text{Hyp}=\sqrt[]{10}mi \\ \text{Opp}=xmi \\ \text{Adj}=3mi \end{gathered}[/tex]Substituting the values into the Pythagorean theorem formula above,
[tex]\begin{gathered} (\sqrt[]{10})^2=x^2+3^2 \\ 10=x^2+9^{} \\ \text{Collect like terms} \\ x^2=10-9 \\ x^2=1 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{1} \\ x=1 \end{gathered}[/tex]The missing side, x is 1mi
Answer is D
Drag the red and blue dots along the x-axis and y-axis to graph -3x+4y=24−3x+4y=24.
Answers
The graph intersect y axis at (0, 6) and x axis at (0, -8).
What is graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
-3x+4y=24
Now, plotting the given graph
Thus, the graph intersect y axis at (0, 6) and x axis at (0, -8)
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are the ratios 19:20 and 3:4 equivalent?
Answers
Answer:
no
Step-by-step explanation:
The ratios 19:20 and 3:4 are not equivalent. Both of them are in their simplest form.
Find the slope of the line passing through the points (-4, 3) and (-4,-5).
slope:
Find the slope of the line passing through the points (-2, -9) and (3, -9).
slope:
Answers
y2 - y1 / x2 - x1
#1: (-5)-3 / (-4)-(-4) = Undefined
#2: (-9)-(-9) / 3-(-2) = Zero (0)
A cube with side length 2 cm sits inside a rectangular prism with width = length
of 9 cm and a height of 4 cm. If the prism is filled with water until the cube is
totally covered (assuming no water goes into the cube), what is the volume (in
mL) used?
Answers
Side of the cube = 2 cm
Width of the rectangular prism = 9 cm
Length of the rectangular prism = 9cm
Height of the rectangular prism = 4 cm
Now,
The volume of total water (submerged cube)
= width of the rectangular prism x length of the rectangular prism x height of the cube
= 9 x 9 x 2 = 162 cm^3
As we know that 1 cm^3 = 1ml
So,
162 cm^3 = 162 ml
Hence the volume of water required to fill the prism such that the cube is submerged is 162 ml.
What is a Rectangular prism?The top, bottom, and lateral faces of a rectangular prism are all rectangles, ensuring that all of the pairings of opposite faces are congruent. A rectangular prism is a three-dimensional structure with six faces. A rectangular prism contains volume and surface area, just like any other three-dimensional structure. Cuboid is another name for a rectangular prism. It has a total of 6 faces, 3 pairs of which are identical opposite faces, making a rectangular prism's opposed faces all the same.The object has three dimensions: height, width, and length. Real-world examples of rectangular prisms include rectangular tissue boxes, notebooks for school, computers, fish tanks, huge buildings like rooms and storage sheds, as well as rectangular cargo containers.To learn more about rectangular prism, refer to:
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Henry paid $32 to rent a table saw for a
two-day period. The maximum length of
time a customer can rent the saw is 10 days
Which equation can be used to find c, the
cost of renting the table saw for the
maximum number of days?
Answers
The equation to find C = no. of max day × rent of one day
The cost of renting table saw for max day = 160$
How to find rent for max days :
Henry paid 32$ for two days ,
so for 1 day = 32/2 = 16$
$16 is rent of table for one day.
The maximum length of time a customer can rent the saw is 10 days.
so, need to find rent for 10 days,
Cost of renting the table saw for 10 day = 10 × 16$
= 160$
How to calculate percentage :
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc.The formula used to calculate percentage is: (value/total value)×100%.To find 15% of 100, rewrite the 15% as 0.15. Then just multiply 0.15 x 100, to get the solution of 15.To learn more about Calculating rent refer :
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Help find the value of x due today
Answers
Answer:if that is 68 get should be 68 degrees too
Step-by-step explanation:
Step-by-step explanation:
68+68+y=180
136+y=180
y=180-136
y=44°
T°=90-44
T°=46°
x+x+46=180
2x=180-46
2x=136
x=136÷2
x=38°
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $11 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)
Answers
Plan 1 is more economical than plan 2. 0.04y + 11 > 30
What is inequality?A statement of an order relationship between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to). The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. In mathematics, an inequality depicts the relationship between two non-equal values in an algebraic expression. Inequality signs can indicate that one of the two variables is greater than, greater than or equal to, less than, or less than or equal to another value.Therefore,
We can point to the digit of calls as "y"
From plan 1, the Total monthly charge is $30
From plan 2, the Fix charge is $11 with $0.04 per call
We can express the cost of the "y" call as( $0.04y)
From plan2, The monthly charge can be expressed as (0.04x + 11)
a) Use an imbalance to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
Here, Plan 1 is more economical than plan 2.
0.04y + 11 > 30
Multiply both sides by 100
0.04y . 100 + 11.100 > 30.100
Refine
4 y+1100>3000$
Subtract 1100 from both sides
4 y+1100-1100>3000-1100
Simplify
4 y>1900
Divide both sides by 4
[tex]$\frac{4 y}{4} > \frac{1900}{4}[/tex]
Simplify
y>475
b) in case, more than 375 calls are made, then the economical plan is plan 1
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I dont need the graphing part, just the way you got all the answers
Answers
The properties of the graph are
Direction = Upy-intercept = -12Axis of symmetry = x = 2Min = -16Vertex = (2, -16)Zeros/Roots/x-intercept = -2 and 6How to complete the table?The equation of the function is given as
f(x) = (x - 2)(x + 6)
The above equation is a quadratic function.
Next, we plot the equation on a graph (see attachment)
Set x = 0 to determine the y-intercept
y-intercept = (0 - 2)(x + 6)
y-intercept = -12
Expand the function to determine the symmetry axis
f(x) = x^2 - 2x + 6x - 12
Differentiate and set to 0
2x - 2 + 6 = 0
This gives
x = -2 --- axis of symmetry
Substitute x = -2 in the function to calculate the vertex/Min/Max
f(-2) = (-2 - 2)(-2 + 6)
f(-2) = -16
This means that
Direction = Up, Min = -16 and Vertex = (2, -16)
Set the function to 0 to determine the roots
(x - 2)(x + 6) = 0
Solve for x
x = 2 and x = -6
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