Question

ou are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor(the observatory) is 82°. If the total height of the building is another 123 meters above the 86th floor, what is the total height of the building?

Answer 1

443.2m

Explanation:

Given in the question that,

distance from building to me = 45m

angle of elevation = 82°

building is 123 m + x m high

If we closely observe then this situation make a right angle triangle and we will use trigonometry identity to solve the question.

Step 1

tan(82) = y / 45

y = 45tan(82)

y = 320.2 m

Step 2

Hence the height of building is y + 123m. So, plug the value of y in this

320.2 + 123 = 443.2