You are 55ft from a tree. The angle of elevation from your eyes, which are 4.5 ft off the ground,to the top of the tree is 61 degrees. To the nearest foot, how tall is the tree?
as usual, draw a diagram. If the tree has height h,
(h-4.5)/55 = tan61°
Approximately 104 feet.
To solve this problem, we can use trigonometry. We will use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle.
Given:
Distance from the tree (adjacent side) = 55ft
Height of the observer's eyes from the ground (opposite side) = 4.5ft
Angle of elevation to the top of the tree = 61 degrees
We can set up the equation as:
Tan(61 degrees) = height of the tree / distance from the tree
Let's solve for the height of the tree:
Tan(61 degrees) = height of the tree / 55ft
Using a scientific calculator, we can find the value of tangent(61 degrees) is approximately 1.874.
1.874 = height of the tree / 55ft
Next, let's isolate the height of the tree:
Height of the tree = 1.874 * 55ft
Height of the tree ≈ 103.07ft
Therefore, to the nearest foot, the height of the tree is approximately 103ft.
To solve this problem, you can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the height of the tree would be the opposite side and the distance from you to the tree would be the adjacent side. So we have:
Tangent of(angle) = Opposite/Adjacent
Tangent(61 degrees) = Height_of_the_tree/Distance_to_the_tree
We know that the distance to the tree is 55 ft and the height of your eyes above the ground is 4.5 ft.
So, let's calculate the height of the tree:
Tangent(61 degrees) = Height_of_the_tree/55 ft
To find Height_of_the_tree, we need to isolate it, so we can rearrange the equation:
Height_of_the_tree = 55 ft × Tangent(61 degrees)
Now, let's calculate it:
Height_of_the_tree = 55 ft × Tan(61 degrees)
Using a calculator, the tangent of 61 degrees is approximately 1.931.
Height_of_the_tree = 55 ft × 1.931 = 106.21 ft
Rounding to the nearest foot, the height of the tree is approximately 106 ft.