Question

A child lies on the ground and looks up at the top of a 9-ft tree nearby. The child is 13 ft away from the tree. What is the angle of elevation from the child to the top of the tree? Round to the nearest whole degree.
35°

55°

46°

44°

Answer 1

Draw a right triangle to represent the problem.
The vertical height of the triangle is 9 ft, and it represents the tree.
The horizontal length, at the bottom of the tree is ground level and has a length of 13 ft.

Let x =  angle of elevation.

By definition,
tan x = 9/13 = 0.6923
x = arctan(0.6923) = 34.7 deg. = 35 deg (approx)

Answer: 35°