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?

443.2m

Step-by-step 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