Question

If YV = 28 in, find the length of the major arc VYX. Round to the nearest tenth ( one decimal place).

Answer 1

Answer:

$VYX=84.3in$

Step-by-step explanation:

Given

$YV = 28in$

$\angle WZX = 15^\circ$

See attachment

Required

Determine the length of $VYX$

First, calculate the major angle VZX

$\theta = \angle VZX = 360 - \angle WZX$

$\theta = \angle VZX = 360 - 15$

$\theta = \angle VZX = 345$

$\theta = 345$

The length of arc VYX, is:

$L=\frac{\theta}{360} * 2\pi r$

Where

$r = \frac{1}{2} * Diameter$

$r = \frac{1}{2} * YV$

$r = \frac{1}{2} * 28$

$r = 14$

So:

$L=\frac{\theta}{360} * 2\pi r$

$L=\frac{345}{360} * 2 * \frac{22}{7} *14$

$L=\frac{345}{360} * 2 * 22 *2$

$L=\frac{345* 2 * 22 *2}{360}$

$L=\frac{30360}{360}$

$L=84.3in$

Hence, the length of VYX is:

$VYX=84.3in$