A tower stands on level ground. Two points on a line through its foot lie on the same side of it…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A tower stands on level ground. Two points on a line through its foot lie on the same side of it, m apart. The angle of elevation of the top is at the farther point and at the nearer point. Find the height of the tower and the distance of the nearer point from the foot.
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 equations. Let be the nearer distance. Then and .
Step 2. Solve. , so and m.
Step 3. The height. m.
Check. m.
Answer: the tower is m tall, and the nearer point is m from its foot.
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