Question

looking up, deon sees two hot air balloons in the sky as shown. he determines that the lower hot air balloon is 810 meters away, at an angle of 19° from the vertical. the higher hot air balloon is 935 meters away, at an angle of 15° from the vertical. how much higher is the balloon on the right than the balloon on the left? do not round any intermediate computations. round your answer to the nearest tenth. note that the figure below is not drawn to scale.

Explanation:

Step1: Calculate the height of the lower balloon

Use the cosine function. For the lower balloon, the distance from Deon is \(d_1 = 810\) meters and the angle from the vertical is \(\theta_1=19^{\circ}\). The height \(h_1\) of the lower balloon is given by \(h_1 = 810\cos(19^{\circ})\).

$$h_1=810\times\cos(19^{\circ})\approx810\times0.9455 = 765.855$$

Step2: Calculate the height of the higher balloon

For the higher balloon, the distance from Deon is \(d_2 = 935\) meters and the angle from the vertical is \(\theta_2 = 15^{\circ}\). The height \(h_2\) of the higher balloon is given by \(h_2=935\cos(15^{\circ})\).

$$h_2 = 935\times\cos(15^{\circ})\approx935\times0.9659=903.0165$$

Step3: Find the difference in heights

Subtract the height of the lower balloon from the height of the higher balloon. Let \(\Delta h=h_2 - h_1\).
\(\Delta h=903.0165 - 765.855=137.1615\)

Answer:

\(137.2\) meters