Question

On a windy day, a 90 foot rope tightly secures a hot air balloon to a stake in the ground. From the balloon, the angle of depression of the stake is 62º. Find the height of the balloon to the nearest foot.

List your knowns and unknowns.
Solve the problem. Make sure your answer contains units and is labeled clearly.
Check your answer.
Write 2-4 sentences explaining your solution/checking process.

Answer 1

• 79 ft

Explanation:

Balloon - B, stake - S, point at ground - G

Given:

• BS = 90 ft
• m∠BSG = 62°
• BG = x

Use sine and solve for x:

• BG/BS = sin ∠BSG
• sin 62° = x / 90
• x = 90 sin 62 deg
• x = 79 ft (rounded)