The angle of elevation from a car to the top of an apartment building is 48 degrees. If the angle from another car that is 22 feet directly in front of the first car is 64 degrees. How tall is the building? I know it involves trig, but after an hour of thought i give up on guessing.

Answers

Answer 1

Answer:

The required height of the building is 53.31 feet.

What is a right angle triangle?

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

Angle of elevation from the first car A to the top of the apartment building = 48 degrees,

Angle of elevation from the second car B to the top of the apartment building = 64 degrees.

Also, car B is 22 feet above the car A.

Let the height of the building is h feet.

And distance from the car B to the building is x feet.

Use formula of tan θ,

tan 64 = h / x

2.050 = h/x

x = h / 2.050 (1)

And tan 48 = h / x + 22
1.1106 = h / x+ 22 (2)

By solving equation (1) and (2)

1.1106 = h / (h/2.050 + 22)

1.1106 = 2.050h / h + 45.1

1.1106h + 50.08 = 2.050h

0.9394 h = 50.08

h = 53.31

The height of the building is 53.31 feet.

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Answer 2

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