Question

A student standing on top of a building sees a bird flying that is 25ft away and 20 ft above the top of the building. The student also sees a car on the ground at and angle of depression 70°. The car is directly below the flying bird.A diagram of the situation is shown below

Answer 1

Answer: The height of the building is 41.2 ft

Explanation:

Here we want to find the height of the building.

To do so, the first step is to find the horizontal distance between the student and the car/bird (which represents the common cathetus between the two triangle rectangles).

For the top triangle rectangle, we know one cathetus and the hypotenuse, and we can use the Pythagorean's theorem to find the other cathetus.

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse.

Then we have:

20^2 + B^2 = 25^2

B^2 = 25^2 - 20^2

B = √( 25^2 - 20^2) = 15

Then the horizontal distance between the student and the car is 15ft, and we also know the angle at which this cathetus is adjacent, the angle is 70°.

Then we can use the relationship:

Tan(A) = (opposite cathetus)/(adjacent cathetus)

Where the opposite cathetus woud be the height of the building, then:

Tan(70°) = H/15ft

Tan(70°)*15ft = H = 41.2 ft