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?

Question

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?

Answer 1

First, we need to convert Shaina's height into feet. Since 1 foot = 12 inches, Shaina's height is 5.5 feet.

Let's call the height of the tree h.

Using the tangent ratio: tan(68 degrees) = h / 20 feet

tan(68 degrees) = h / 20

h = 20 * tan(68)

h ≈ 45.7 feet

Therefore, the height of the tree is approximately 45.7 feet.