Question

What is the degree measure of an arc 4 pie ft long in a circle of radius 10 ft

Answer 1

`\blue{ \theta = 72 \degree }`

Explanation:

The formula to find length of an arc is :

`arc \: \: length \: = ( \theta)/(360) * 2\pi \: r`

Here,

`arc \: \: length = 4\pi \\ r = radius = 10ft \\`

`\red{\theta = } \red{measure \: of \: the \: angle}`

We can solve for measure of the angle of the arc by using the above formula.

Let us solve now.

`arc \: \: length \: = ( \theta)/(360) * 2\pi \: r \\ 4\pi= ( \theta)/(360) * 2\pi \: * 10 \\ 4\pi = ( \theta)/(360) * 20\pi \\ 360 * 4\pi = 20 \pi\theta\\ 1440\pi = 20\pi \theta \\ (1440\pi)/(20\pi) = (20\pi \theta)/(20\pi) \\ 72 \degree = \theta`