The angle of elevation at the top of a building is 34 degrees. at a point 80 feet closer , the angle of elevation to the top of the same building is 45 degrees. approximate the height of the building.

According to the diagram, AB is the building.

Let distance BC= x CD= 80 ft

So distance BD= x + 80

In triangle ABD,

anlge ACB = 45 degree

So Triangle ACB is an isosceles triangle.

So AB = BC = x

Consider triangle ABD,

tan (34) =

0.6745 =

Cross multiply

0.6745 (x + 80 ) = x

0.6745 x + 53.46 = x

53.46 = x - 0.6745x

53.46 = 0.3255 x

Now divide both side by 0.3255

x = 164.24 ft

So height of the building is 164 ft approximately

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