Law of Sines Homework Help

Question

Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is 700 ft high. From the roof of the shorter building, the angle of elevation to the top of the taller building is 78° and the angle of depression to the base of the taller building is 62°.

1. What is the height of the shorter building?
2. What is the distance between the two buildings?

Answer 1

Draw and label a diagram!

d represents the distance between the two

h represents the height of the smaller

h represents the bottom of the taller opposite 62°

700 - h represents the top of the taller opposite 78°

tan 78° = (700 - h) / d

d tan 78 ° = 700 - h

d = (700 - h) / tan 78°

tan 62° = h / d

d tan 62 = h

d = h / 62°

Set the two equal and solve for h

Use the same tangent equations yet isolate h and solve for d.