Approximate the length using the formula for arc length. Round to the nearest meter.
-A tree 460 m away subtends an angle of 2°. Find the height of the tree.
A)32 m
B)13 m
C)16 m
D)35 m

Question

Quizplus · Accepted Answer

The formula for arc length is $s = r\theta$, where $s$ is the arc length, $r$ is the radius (or distance to the object), and $\theta$ is the angle in radians. First, convert 2° to radians: $2° \times \frac{\pi}{180°} = \frac{\pi}{90}$. Then, use the formula with $r = 460$ m and $\theta = \frac{\pi}{90}$ radians to find $s$: $s = 460 \times \frac{\pi}{90} \approx 16$ m.

Approximate the Length Using the Formula for Arc Length