Solve the problem.
-At an altitude of $3800 \mathrm { ft }$, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 5 miles away by land? (Round your answer to the nearest tenth of a degree.)
A) $89.9 ^ { \circ }$
B) $88.9 ^ { \circ }$
C) $8.2 ^ { \circ }$
D) $9.2 ^ { \circ }$

Question

Quizplus · Accepted Answer

To solve this, we can use trigonometry. The distance to the airport (5 miles) and the altitude (3800 ft) form a right triangle. First, convert 5 miles to feet: $5 \text{ miles} \times 5280 \text{ ft/mile} = 26400 \text{ ft}$. Then, use the tangent function, where the angle of glide $\theta$ satisfies $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3800}{26400}$. Solving for $\theta$ gives $\theta \approx 8.2^\circ$.

Solve the Problem 3800ft3800 \mathrm { ft }3800ft , the Engine on a Small Plane Fails

Solve the Problem $3800 \mathrm { ft }$ , the Engine on a Small Plane Fails