A developer is building a scale model of the city. From the roof of an apartment complex, the developer points two lasers at the taller office building across the street. The first laser points to the base of the building and the second laser points to the top of the building. The first laser beam has an angle of depression of 36° and is 155.7 feet long. The second has an angle of elevation of 32° and is 148.6 feet long. How tall is the office building? How far apart are the apartment complex and the office building? Round your answers to the nearest foot.

The two laser lights with the length of the taller office building, L form a triangle with sides 155.7 feet, 148.6 feet and L with angle 36° + 32° = 68° facing the taller office building.

We use the cosine rule to find the length of taller office building.

So, L² = 155.7² + 148.6² - 2(155.7)(148.6)cos68°

L² = 24242.49 + 22081.96 - 46,274.04(0.3746)

L² = 46324.45 - 17334.56

L² = 28989.89

L = √28989.89

L = 170.26 ft

L ≅ 170 ft

b. How far apart are the apartment complex and the office building?

Using one of the lights, the distance between the buildings, d, the laser light(being the hypotenuse side) and the building (being the opposite side)form a right angled triangle.

So, using the 155.7 feet light at 36 angle,

cos36 = d/155.7

d = 155.7cos36

d = 155.7(0.8090)

d = 125.96 ft

d ≅ 126 ft