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In one city there are two hotels that are opposite each other, namely Hotel A and Hotel B. The angle of elevation of the top of Hotel A from the foot of Hotel B is 30° and the angle of elevation of the top of Hotel B from the foot of Hotel A is 60°. If Hotel B is 75 m high, find the height of Hotel A.

Sagot :

The height of hotel A is approximately 25 m.

The illustration above will form 2 right angle triangle.

The both triangles have the same adjacent side.

let's use the information of hotel B to find the adjacent side of the triangle.

The opposite side of the triangle is the height of hotel B(75m)

using trigonometric ratio,

tan 60°  = opposite / adjacent

tan 60° = 75 / x

x = 75 / tan 60°

x = 43.3025404157 m

x ≈ 43.30 m

Height of hotel A can be found as follows:

The height is the opposite side of the right angle triangle. Therefore,

tan 30° = h / 43.30

h = tan 30° × 43.30

h = 24.9992666559

height ≈ 25 m

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