HardMathematicsHigh School (9–10)GeneralTrigonometry › Heights and DistancesNumericalword problemOlympiadSAT
From a window 14 m above the ground, the angle of depression of the foot of a tower is 30° and the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
From a window m above the ground, the angle of depression of the foot of a tower is and the angle of elevation of its top is . Find the distance of the tower from the building and the height of the tower.
Need a reminder? The key ideaShow
When one object stands on another, both lines of sight end on one vertical line, so the two triangles share the base . The length of the upper object is a difference of two heights, . An angle of depression equals the angle of elevation seen from the other end.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The distance. In the triangle below the window, , so m.
Step 2. The part above the window. , so m.
Step 3. The tower. It is m tall.
Check. The two parts, m below the window and m above it, add up to the whole tower.
Answer: the tower is m from the building and m tall.
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