Question

Mallory is standing on top of an apartment building in New York City. She knows that her apartment building is exactly 350 feet away from the Macy’s store. Wanting to know the height of Macy’s, Mallory measures the angle of elevation to the top of the store from her position and finds it is 36°. When she measures the angle of depression to the base of the store, she finds that it is 64°. Using this information, find the height of Macy’s to the nearest tenth of a foot.

Answer 1

Answer:

971.9 ft

Step-by-step explanation:

$\theta_1= 64^{\circ}$

$\theta_2=36^{\circ}$

b = Base = 350 ft

$\tan\theta_1=\dfrac{P_1}{b}\\\Rightarrow P_1=b\tan\theta_1\\\Rightarrow P_1=350\times \tan64^{\circ}$

$\tan\theta_2=\dfrac{P_2}{b}\\\Rightarrow P_2=b\tan\theta_2\\\Rightarrow P_2=350\times \tan36^{\circ}$

Height of Macy's is given by

$P_1+P_2=350\times \tan64^{\circ}+350\times \tan36^{\circ}\\\Rightarrow P_1+P_2=350(\tan64^{\circ}+\tan36^{\circ})\\\Rightarrow P_1+P_2=971.9\ \text{ft}$

The height of Macy's is 971.9 ft