Question

question 1 of 20
the arc corresponding to a central angle of 65° in a circle of radius 10 feet measures ____ feet. round your answer to two decimal places.

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc \( s \) of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( s=\frac{\theta}{360^{\circ}}\times2\pi r \). Here, \( \theta = 65^{\circ} \) and \( r = 10 \) feet.

Step2: Substitute the values into the formula

Substitute \( \theta = 65^{\circ} \) and \( r = 10 \) into the formula: \( s=\frac{65^{\circ}}{360^{\circ}}\times2\pi\times10 \).
First, simplify \( \frac{65}{360}\times20\pi \). \( \frac{65\times20}{360}\pi=\frac{1300}{360}\pi=\frac{65}{18}\pi \).
Then, calculate the numerical value: \( \frac{65}{18}\times\pi\approx\frac{65}{18}\times3.14159\approx11.34 \) (rounded to two decimal places).

Answer:

\( 11.34 \)