Question

the angle of elevation from the top of one building to another is 26 degrees. if the shorter building is 400 feet tall and the buildings are 1500 feet apart , how tall is the other building ?

Answer 1

Draw a diagram. Then use tan(x) to find the remainder height of the taller building.

Answer 2

The other building(the long one) is 1131.55 feet tall.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Angle of elevation = 26°

Shorter building height = 400 feet

Distance between the buildings = 1500 feet

As we can see in the figure AD is the height of a long building.

AD = AE + DE

AD = 400 + DE   (shorter building height AE = 400 ft)

Now we have to calculate the length of the DE

For this, from the right angle triangle ∠DCE = 26° and EC = AB = 1500 ft

$\rm tan 26\° = \frac{DE}{EC} \\\\\rm tan 26\° = \frac{DE}{1500}$  

DE = 1500(tan26°)

DE = 1500×0.4877

DE = 731.55 ft

Now AD = 400 + 731.55 ⇒ 1131.55 feet

Thus, the other building(the long one) is 1131.55 feet tall.

Know more about trigonometry here:

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