Willow stood due south of a totem pole, 21.0m from its base, and measured the angle of elevation of the top of the pole as 58 degrees. Winston stood due east of the totem pole and measured the angle of elevation of the top of the pole as 49 degrees. How far is Winston from the base of the totem pole to the nearest tenth of a metre?

Question

Ruffer

Mathematics

22 December, 02:46

Willow stood due south of a totem pole, 21.0m from its base, and measured the angle of elevation of the top of the pole as 58 degrees. Winston stood due east of the totem pole and measured the angle of elevation of the top of the pole as 49 degrees. How far is Winston from the base of the totem pole to the nearest tenth of a metre?

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Andrea Ruiz · Answer 1

29.2 meters

Step-by-step explanation:

First we can find the height of the totem using the tangent relation of the angle of elevation, where the opposite side to the angle is the height of the totem, and the adjacent side to the angle is the distance to the totem base:

tangent (58) = h / 21

h = 1.6 * 21 = 33.6 meters

Now, we do the same thing with the angle of 49, now to find the distance to the totem base:

tangent (49) = 33.6 / d

d = 33.6 / 1.1504 = 29.21 meters

Rounding to nearest tenth, we have d = 29.2 meters