How tall is a building that casts a 78-ft shadow when the angle of elevation of the sun is 31°?

49.91 feet

Step-by-step explanation:

We can solve the exercise by means of the trigonometric ratio of the tangent, since we know the angle between both legs which in this case is the height and length of the shadow, therefore we have to:

tan ° A = opposite / adjacent

° A = 31; adjacent (height) = 78 ft

replacing

tan 34 ° = x / 74

x = tan 34 ° * 74

x = 49.91

that is, the distance from the shadow is 49.91 feet