HardMathematicsHigh School (9–10)GeneralTrigonometry › Heights and DistancesNumericalword problemOlympiadSAT
A boy whose eyes are 1.4 m above the ground looks at the top of a building at an angle of elevation…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A boy whose eyes are m above the ground looks at the top of a building at an angle of elevation of . He walks m straight towards the building, and the angle becomes . How tall is the building, and how far from it is the boy now?
Need a reminder? The key ideaShow
Two observation points on a line through the foot of a tower give two right triangles. On the same side, and , so . On opposite sides the distances add: . The nearer point sees the larger angle.
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 height above eye level. Let it be . Then m.
Step 2. The building. m.
Step 3. The distance now. m, so the boy is m from the building.
Check. The first distance was m, and m.
Answer: the building is m tall, and the boy is m from it.
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