Question

If xh=10 feet and mxy =100 degrees then determine the arc length of xy

Answer 1

Answer:

The arc length XY is equal to $\frac{50}{9}\pi\ ft$  or $17.4\ ft$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the circumference of the circle H

The circumference is given by the formula

$C=2 \pi r$

we have

$r=xh=10\ ft$

substitute

$C=2 \pi (10)\\C=20\pi\ ft$

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of the arc xy if the central angle is equal to 100 degrees

Remember that

$m\angle XHY=arc\ XY=100^o$ ---> by central angle

$\frac{20\pi}{360^o}=\frac{x}{100^o}\\\\x=20\pi(100)/360\\\\x=\frac{2,000}{360}\pi\ ft$

Simplify

$x=\frac{50}{9}\pi\ ft$ ----> exact value

To find out the approximate value

assume

$\pi=3.14$

substitute

$x=\frac{50}{9}(3.14)=17.4\ ft$ ----> approximate value

therefore

The arc length XY is equal to $\frac{50}{9}\pi\ ft$  or $17.4\ ft$