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
[tex]\tan \left(17.9^{\circ}\right)=\frac{a}{122 \mathrm{ft}}[/tex]
[tex]a=122 \times \tan 17.9^{\circ}=122 \times 0.32299=39.4[/tex]
Similarly,
[tex]\tan \left(29.5^{\circ}\right)=\frac{b}{122 f t}[/tex]
[tex]b=122 \times \tan \left(29.5^{\circ}\right)=122 \times 0.56577=69.02[/tex]
The nearest tenth of a foot, the balloon rise during the period, as below
69.02 – 39.4 = 29.62 ft.
