Question

From the roof of a skyscraper, Aisha spots a car at an angle of depression of 51° from the roof of the skyscraper. If the skyscraper is 78 m high how far away is the car from the base of the skyscraper, correct to the nearest minute?

Answer 1

Answer: 63 meters

Step-by-step explanation

The diagram is shown below.

Point A is the base of the skyscraper. Point B is the location of Aisha's eye.

Point C is the location of the car. Point D helps set up the angle of depression. This is where Aisha starts looking horizontally, and then rotates her viewpoint 51 degrees downward to spot the car.

Notice how the angle of elevation is equal to this, because of alternate interior angles.

Focus entirely on triangle ABC. Ignore point D.

tan(angle) = opposite/adjacent

tan(C) = AB/AC

tan(51) = 78/x

x*tan(51) = 78

x = 78/tan(51)

x = 63.16315 approximately

I'm assuming the instructions saying "nearest minute" should read "nearest meter". If so, then 63.16315 rounds to 63 meters as the final answer.