Question
Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is 30∘, find the length of the second pole.
Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is 30∘, find the length of the second pole.
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Solution
Refer to the following figure:
AB is the longer pole of length 10m. ED is the shorter pole. Let the lengths be broken down as shown.
In ΔABE, sin30∘ ⇒ x=3
Since x + y = 10 and x = 3, y = 7m.
Observe that BC = y = ED = length of the shorter pole = 7m.
Refer to the following figure:
AB is the longer pole of length 10m. ED is the shorter pole. Let the lengths be broken down as shown.
In ΔABE, sin30∘ ⇒ x=3
Since x + y = 10 and x = 3, y = 7m.
Observe that BC = y = ED = length of the shorter pole = 7m.
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