Acentral angle theta in a circle of radius 7 m is subtended by an arc of length 8 m. find the measure of theta in degrees. (round your answer to one decimal theta = find the measure of theta in radians. theta = rad.

The measure of central angle theta in a circle of radius 7 m and subtended by an arc of length 8 m is 65. 4°(degrees) or  1.141445 radians

The central angle is unknown and its is subtended by an arc of length 8m .

Therefore,

Using length of arc formula,

length of arc = ∅  /360 × 2πr

where

∅ = angle

r = radius = 7m

length of arc = 8m  

8 = ∅ /360 × 2 × 7 × π

8 = ∅ /360 × 14π

14π∅ = 2880

∅ = 2880 / 14π

∅ = 65.3912348499

∅ ≈ 65. 4°(degrees)

∅ = 1.141445 radians

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In degrees , The measure of

In radians , the measure of  .

Step-by-step explanation:

We know that the formula for length of arc is given by :-

, where = Central angle subtended by arc.

r= radius of the circle.

As per given , we have

Radius of circle : r=7 m

Length of arc : l=  8 m

Substitute these values in the above formula , we get

Hence, the measure of .

To convert it into degrees we multiply it with

The measure of

Hence, the measure of

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