From a hot-air balloon, Lillian measures a 38∘ angle of depression to a landmark that’s 704 feet away, measuri

Question

From a hot-air balloon, Lillian measures a 38∘ angle of depression to a landmark that’s 704 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

GPT-5 mini · Answer

Let h be the balloon's height. Angle of depression = angle of elevation, so

h = 704 · tan(38°) ≈ 704 · 0.7812856 ≈ 550.0 ft.

The balloon is about 550.0 feet above the ground.

From a hot-air balloon, Lillian measures a 38∘ angle of depression to a landmark that’s 704 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

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