Trigonometry Word Problem

Question

From a point on the floor, the angle of elevation to the top of a door is 48°, while the angle of elevation to the ceiling above the door is 59°. If the door is 8 ft tall, what is the vertical distance from the floor to the ceiling?

Answer 1

Draw a figure!

The distance from the point on the floor to the edge of the door is x.

cot 48 = x/8 => x = 8 cot 48

The distance to the ceiling at the point x = y

tan 59 = y/x => y = x tan 59 = 8 cot 48 tan 59