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Answer :
Draw a diagram. Then use tan(x) to find the remainder height of the taller building.
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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
[tex]\rm tan 26\° = \frac{DE}{EC} \\\\\rm tan 26\° = \frac{DE}{1500}[/tex]
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.
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