An aerial photograph is taken of a building. The photograph is made when the angle of elevation of the sun is 34 degrees. The shadow is determined to be 80 feet long. How tall is the​ building?

Answer 1

To find the height of the building, we can use trigonometry and the given information.

Let's assume the height of the building is h feet. The angle of elevation of the sun is 34 degrees, so the angle between the shadow and the horizontal is also 34 degrees.

Using the tangent function, we have:

tan(34 degrees) = h / 80 feet

h = 80 feet * tan(34 degrees)
h = 80 feet * 0.6859
h ≈ 54.87 feet

Therefore, the height of the building is approximately 54.87 feet.