Answer:
a. 170 ft b. 126 ft
Step-by-step explanation:
a. How tall is the office building?
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