# trigo

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from the top of 90 meters high building it is observe that the top of another building make a 40 degree angle depression. if two buildings 75 meters apart how tall is the other building?

• trigo -

Draw a diagram. If the top of the 90m tower is A, the top of the shorter building is B, draw a horizontal line from B to the 90m tower. Label the intersection C.

Now, ABC is a right triangle, and angle A is 45°. The difference in heights is side b. The distance between the buildings is a.

a/b = tan 50° = 1.192
b = 75/1.192 = 62.92m

So, the shorter building is 90-62.92 = 27.08m tall.

• trigo -

oops A is 50° (90° - angle of depression)

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