Question

​ hot-air balloon is rising vertically. The angle of elevation from a point on level ground 122 feet from the balloon to a point directly under the passenger compartment changes from 17.9 degrees to 29.5 degrees. How​ far, to the nearest tenth of a​ foot, does the balloon rise during this​ period?

Answer 1

29.62 feet far, to the nearest tenth of a​ foot, does the balloon rise during this​ period

Explanation:

Hot-air balloon is rising vertically, the angle of elevation from a point on level ground = 122 feet (from the balloon)

The passenger compartment changes from = 17.9 degrees to 29.5 degree

              $\tan \left(17.9^{\circ}\right)=\frac{a}{122 \mathrm{ft}}$

              $a=122 \times \tan 17.9^{\circ}=122 \times 0.32299=39.4$

Similarly,

              $\tan \left(29.5^{\circ}\right)=\frac{b}{122 f t}$

              $b=122 \times \tan \left(29.5^{\circ}\right)=122 \times 0.56577=69.02$

The nearest tenth of a foot, the balloon rise during the period, as below

               69.02 – 39.4 = 29.62 ft.