From a hot-air balloon, Juan measures a 36degrees ∘ angle of depression to a landmark that’s 602 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.
Question
From a hot-air balloon, Juan measures a 36degrees ∘ angle of depression to a landmark that’s 602 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.
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (the height of the balloon) to the adjacent side (the horizontal distance to the landmark).
The formula for tangent is:
tan(θ) = opposite/adjacent
We know that the angle of depression (θ) is 36 degrees and the adjacent side (the horizontal distance to the landmark) is 602 feet. We want to find the opposite side (the height of the balloon), which we'll call h.
Rearranging the formula to solve for h gives us:
h = tan(θ) * adjacent
Substituting the given values into the formula gives us:
h = tan(36) * 602
Calculating this gives us:
h ≈ 434.4 feet
So, the balloon is approximately 434.4 feet above the ground.
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