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

Step-by-step 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 * \tan 17.9^(\circ)=122 * 0.32299=39.4`

Similarly,

`\tan \left(29.5^(\circ)\right)=(b)/(122 f t)`

`b=122 * \tan \left(29.5^(\circ)\right)=122 * 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.