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

Answer:

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:

$l=\frac{\theta}{360\degree}\times2\pi r$

Substitute the known values:

$32=\frac{a}{360}\times2\times3.14\times29$

Solve the equation for a:

$\begin{gathered} \text{ Cross multiply} \\ a\times2\times3.14\times29=32\times360 \\ \implies a=\frac{32\times360}{2\times3.14\times29} \\ a\approx63.3\degree \end{gathered}$

The measure of angle a is 63.3 degrees.