Use trigonometric ratios to solve the following problem. Shaina, who is 67.2 inches tall, is standing 240 inches from the base of a tree when she sees a pileated woodpecker at the top of the tree. The bird is at an angle of elevation of 68 degrees above Shaina’s line of sight. What is the height of the tree?
First, we can construct a right triangle with Shaina's height representing the length of the adjacent side (67.2 inches), the distance from Shaina to the tree representing the length of the hypotenuse (240 inches), and the height of the tree representing the length of the opposite side (which we want to find).
Using the tangent ratio (opposite/adjacent = tan(angle)), we can set up the equation:
tan(68 degrees) = height of tree / 67.2 inches
Solving for the height of the tree:
height of tree = 67.2 inches * tan(68 degrees)
height of tree = 67.2 inches * 2.42705
height of tree ≈ 163.13 inches
Therefore, the height of the tree is approximately 163.13 inches.