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

Answer:

$82.43\ \text{feet}$

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

$\tan\theta=\dfrac{p}{b}\\\Rightarrow p=b\tan\theta\\\Rightarrow p=42\tan63^{\circ}\\\Rightarrow p=82.43\ \text{feet}$

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