Solve the problem.
-A hot-air balloon is rising vertically 10 ft/sec while the wind is blowing horizontally at 4 ft/sec. Find the angle that the balloon makes with the horizontal.
A)68.2°
B)34.3°
C)21.8°
D)52.8°

Question

Quizplus · Accepted Answer

The angle $\theta$ that the balloon makes with the horizontal can be found using the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side is the vertical speed (10 ft/sec) and the adjacent side is the horizontal speed (4 ft/sec). Thus, $\tan(\theta) = \frac{10}{4} = 2.5$. Solving for $\theta$ gives $\theta = \tan^{-1}(2.5) \approx 68.2^\circ$.

Solve the Problem. -A Hot-Air Balloon Is Rising Vertically 10 Ft/sec While the Ft/sec