Approximate the length using the formula for arc length. Round to the nearest meter.
-A television tower $420 \mathrm {~m}$ high subtends an angle of $4 ^ { \circ } 40 ^ { \prime }$. How far away is the tower?
A) $6720 \mathrm {~m}$
B) $5157 \mathrm {~m}$
C) $6760 \mathrm {~m}$
D) $5197 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To find the arc length, convert the angle from degrees and minutes to radians: $4^\circ 40' = 4 + \frac{40}{60} = 4.6667^\circ$. Convert to radians: $4.6667 \times \frac{\pi}{180} \approx 0.0814$ radians. Use the formula for arc length $s = r\theta$, where $r = 420 \mathrm{~m}$ and $\theta = 0.0814$. Thus, $s \approx 420 \times 0.0814 \approx 34.188$. The distance is the radius of the circle, so $r = \frac{420}{0.0814} \approx 5157 \mathrm{~m}$.

Approximate the Length Using the Formula for Arc Length 420 m420 \mathrm {~m}420 m

Approximate the Length Using the Formula for Arc Length $420 \mathrm {~m}$