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?

Question

asked Jul 3, 2022 19.9k views

1 Answer

Antonakos · Answer 1 · 2022-07-07T09:24:03+0000

Answer:

$82.43\ \text{feet}$

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
$82.43\ \text{feet}$ .