Question

A rope is tied to the bottom of a hot air balloon as shown below. The rope makes an angle of 35 degrees with the ground distant of 75 feet. How far is the bottom of the balloon from the ground to the nearest foot. (Please show work)

Answer 1

We have a right triangle. We know the hypotenuse (75 ft) and an angle of 35°. We need to find the opposite leg to the angle of 35° (h). The trigonometric function that relates the opposite leg to an angle with the hypotenuse is sine:
sin 35° = (Opposite leg to 35°) / hypotenuse
sin 35° = h/(75 ft)

Solving for h:
(75 ft) sin 35°=h
h=75 sin 35° ft
h=75 (0.573576436) ft
h=43.01823270 ft
h=43 ft

Answer: The bottom of the balloon is 43 ft from the ground