Question

Circle O shown below has a radius of 29 inches. Find, to the nearest tenth of adegree, the measure of the angle, a, that forms an arc whose length is 32 inches.

Answer 1

a=63.3°

Explanation:

Given a circle O in which:

• The radius, r = 29 inches

,

• The length of an arc of the circle = 32 inches

We want to find the measure of the angle that forms the arc.

The length of an arc is calculated using the formula below:

`l=(\theta)/(360\degree)*2\pi r`

Substitute the known values:

`32=(a)/(360)*2*3.14*29`

Solve the equation for a:

`\begin{gathered} \text{ Cross multiply} \\ a*2*3.14*29=32*360 \\ \implies a=(32*360)/(2*3.14*29) \\ a\approx63.3\degree \end{gathered}`

The measure of angle a is 63.3 degrees.