Chelsea is sitting 8 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36°. If her line of sight starts 1.5 feet above ground, how tall is the tree, to the nearest foot?
To find the height of the tree, we can use trigonometry, specifically the tangent function.
Let's refer to the height of the tree as "h."
From Chelsea's line of sight, we can form a right triangle with the tree as the vertical side and the distance from Chelsea to the tree as the horizontal side. The angle of elevation of 36° is opposite the height of the tree and adjacent to the distance from Chelsea to the tree.
First, we need to find the distance from Chelsea to the tree. We are given that Chelsea is sitting 8 feet from the foot of the tree, so the distance is 8 feet.
Next, we can set up the equation using the tangent function:
tan(36°) = h / 8
To find h, we can solve for it:
h = 8 * tan(36°)
Using a scientific calculator or any trigonometric calculator, we can find the value of tan(36°) ≈ 0.7265.
h = 8 * 0.7265
h ≈ 5.812 feet
However, we need to account for the fact that Chelsea's line of sight starts 1.5 feet above the ground, so we need to add this to the calculated height.
Total height of the tree ≈ 5.812 feet + 1.5 feet
Total height of the tree ≈ 7.312 feet
Rounded to the nearest foot, the tree is approximately 7 feet tall.