Height from an angle of elevation
Use tan(angle) = opposite/adjacent to find the height of a structure from a measured distance and angle of elevation. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
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A surveyor stands 18 m from a hydro pole and measures an angle of elevation of 29deg to the top. Find the height of a hydro pole, to one decimal place.
tan(angle) = height / distance
Answer: 10
See one solved, step by step
A surveyor stands 23 m from a construction crane and measures an angle of elevation of 24deg to the top. Find the height of a construction crane, to one decimal place.
tan(angle) = height / distance
📘 Worked solution
1tan(angle) = opposite / adjacent = height / distanceThe angle of elevation, the horizontal distance, and the height form a right triangle.
2height = 23 · tan(24deg)Rearrange to solve for the height, then substitute the known distance and angle.
3= 23 · 0.4452 = 10.2 mEvaluate the tangent ratio (calculator in degree mode), then multiply.
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