Question

in circle u below, vt = 90 inches. what is the length of arc zv? \boxed{}π inches

Explanation:

Step1: Find the radius of the circle

VT is a diameter (since it passes through the center U), so the radius \( r \) is half of VT. Given \( VT = 90 \) inches, then \( r=\frac{90}{2}=45 \) inches.

Step2: Recall the arc length formula

The formula for the length of an arc with central angle \( \theta \) (in degrees) is \( \text{Arc Length}=\frac{\theta}{360^\circ}\times 2\pi r \).

Step3: Substitute the values

Here, \( \theta = 104^\circ \) and \( r = 45 \) inches. Plugging into the formula:
\[

$$\begin{align*} \text{Arc Length of } ZV&=\frac{104^\circ}{360^\circ}\times 2\pi\times 45\\ &=\frac{104}{360}\times 90\pi\\ &=\frac{104\times 90}{360}\pi\\ &=\frac{104}{4}\pi\\ & = 26\pi \end{align*}$$

\]

Answer:

26