In a circle with radius 0.9, an angle measuring 8.9 radians intercepts an arc. Find the length of the arc to the nearest 10th.

Answers

Answer 1

The length of arc to the nearest 10th is 26 units.

A circle is a shape produced by all points in a plane at a specific distance from the center.

Given a circle of radius (r) = 2.9, an angle of 1.8 radians intercepts an arc.

The length of the arc must be determined.

(angle measure / 2) × (circumference of circle) equals arc length

Angle = (8.9 radians) × (180 degrees / π )

We know π = 3.14

Angle = 8.9 ×180 / 3.14

= 1602 / 3.14

= 510.19°

Angle measurement is 510.19 degrees.

Circumference: 2 × π × r

= 2 × 3.14 × 2.9

= 18.212 units

Arc length = (Arc length / 360) × Circumference

= 510.19 / 360 × 18.212

= 9,290.5599 / 360

= 25.81 units

As a result, the length of the are is 25.81 units. Rounding off to nearest tenth, it will be 26 units.

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