Use trigonometric ratios to solve the following problem. Shaina, who is 5 feet, 6 inches tall, is standing 20 feet 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, convert Shaina's height to inches: 5 feet * 12 inches = 60 inches + 6 inches = 66 inches.
Next, we can use the tangent ratio because we have the opposite (height of the tree) and adjacent (distance from the base of the tree) sides of the triangle:
tan(68°) = height of the tree / distance from the base of the tree
tan(68°) = height of the tree / 20 feet
Height of the tree = 20 feet * tan(68°)
Height of the tree ≈ 20 feet * 2.3706
Height of the tree ≈ 47.412 inches
Therefore, the height of the tree is approximately 47.412 feet.