Question

A man on the fifth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street? A) 28 feet B) 55 feet C) 56 feet D) 57 feet

Answer 1

57 ft because drawing it up, we can make a right angled triangle with the right angle between the height of the man in the building and the distance out from the building of the man in the street, and the 35 degrees between the line connecting the man in the street with the man in the building, and the line out from the building of the man in the street. Then, tan of the 35 degree angle is = to opposite (40ft)/adjacent (to solve for). By cross multiplication, the A or adjacent (dist out from the building) = 40/0.7 (0.7 = tan of 35 degrees) so the answer is 57 ft. 

Answer 2

The correct answer is 57 feet. Since this is a right triangle and you know the angle and opposite side and are trying to find the adjacent side you can use tangent. tan  $= \frac{40}{x}$, so  $x = \frac{40}{tan(35)}$.