Question

Two buildings are 60 feet apart cross a street. a person on top of the shorter building finds the angle of elevation of the roof of the taller building to be 20' and the angle of depression of its base to be 35' how tall is the taller building to the nearest foot

Answer 1

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Answer 2

The answer is 64 ft.

You can look at the attached photo to see the scenario. As you can see, there are two right triangles formed by the scenario. So we can do this using trigonometric function;

$Tan\theta=\frac{O}{A}$

Where:

θ = angle

O = Opposite

A = Adjacent

We use this because the problem gives you the angle of elevation and the adjacent side of each triangle. And we are looking for the opposite of each triangle as well.

Using the angle of elevation, we can solve for the height of the other building from the point of the viewer to the top. So we have the top half of the building. Let's solve for it:

$Tan\theta=\frac{O}{A}$

$Tan20=\frac{O}{60ft}$

$(Tan20)(60ft)=O$

$22ft=O$

Now using the angle of depression we can find the height of the building from the base of the other building to the point of the viewer. Let's solve it again:

$Tan\theta=\frac{O}{A}$

$Tan35=\frac{O}{60ft}$

$(Tan35)(60ft)=O$

$42ft=O$

So now we just add the two heights together to get the TOTAL HEIGHT of the building.

42ft + 22 ft = 64 ft