A pole stands on level ground. Two points on a line through its foot, on the same side, are 5 m and…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A pole stands on level ground. Two points on a line through its foot, on the same side, are m and m from the foot. The two angles of elevation of the top add up to . Find the height of the pole and the smaller angle of elevation.
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. Two tangents. The farther point is m away, so . The nearer point is m away, so .
Step 2. Use the right angle. Since , , so .
Step 3. The height. and m.
Step 4. The smaller angle. , so . The other angle is .
Answer: the pole is m tall, and the smaller angle is .
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