Question

From the top of a building 42 feet high, the angle of depression to a car stopped on the ground it is 27°. What is the distance from the car to the base of the building?

Answer 1

`82.43\ \text{feet}`

Step-by-step explanation:

Angle of depression =
`27^(\circ)`

b = Height of building = 42 feet

`\theta=90-27=63^(\circ)`

p = Distance from the car to the base of the building

From the trigonometric identities we get

`\tan\theta=(p)/(b)\\\Rightarrow p=b\tan\theta\\\Rightarrow p=42\tan63^(\circ)\\\Rightarrow p=82.43\ \text{feet}`

The distance from the car to the base of the building is
`82.43\ \text{feet}`.