Approximate the length using the formula for arc length. Round to the nearest meter.
-A television tower $450 \mathrm {~m}$ high subtends an angle of $2 ^ { \circ } 10 ^ { \prime }$. How far away is the tower?
A) $1840 \mathrm {~m}$
B) $11,940 \mathrm {~m}$
C) $11,900 \mathrm {~m}$
D) $1800 \mathrm {~m}$

Question

Quizplus · Accepted Answer

The arc length formula $ s = r\theta $ can be used, where $ r = 450 $ m and $ \theta = 2^\circ 10' = 2.1667^\circ = 0.0378 $ radians. Thus, $ s = 450 \times 0.0378 \approx 17.01 $ m. However, this is not the distance to the tower. The correct approach is to use the tangent function: $ \tan(\theta) = \frac{450}{d} $, solving for $ d $ gives $ d \approx 11,900 $ m.

Approximate the Length Using the Formula for Arc Length 450 m450 \mathrm {~m}450 m

Approximate the Length Using the Formula for Arc Length $450 \mathrm {~m}$