Question

You 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?
A) [45tan(82°) + 123] meters
B) [123tan(82°) + 45] meters
C) [45cos(82°) + 123] meters
D) [123cos(82°) + 45] meters

Answer 1

Answer:

[45tan(82°)+123] meters

A is correct

Step-by-step explanation:

You 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.

OB = 45 m , ∠O= 82°

In Δ OBA, ∠B = 90°

$\tan82^\circ=\dfrac{AB}{OB}$

$\tan82^\circ=\dfrac{AB}{45}$

$AB=45\tan82^\circ$

Top of the building, T at 123 m from A

Total height of building = BA + AT

                                $=45\tan82^\circ+123\text{ meters}$

Hence, The height of building from ground is [45tan82°+123] meters