Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A statue m tall stands on a pedestal. From a point on the ground, the angle of elevation of the top of the pedestal is and of the top of the statue is . Find the height of the pedestal and the height of the top of the statue above the ground.
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.
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 pedestal. Let it be . At , .
Step 2. The statue's top. , so .
Step 3. Solve. , so m.
Step 4. The top of the statue. m above the ground.
Answer: the pedestal is m tall, and the top of the statue is at m.
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