a tower 61 m high is located 44 meters from a tall tree.from the top of the tree.the angle of elevation to the tower is 36 degrees. how tall is the tree?
As always, draw a diagram.
If the tree has height h, then
(61-h)/44 = tan 36°
To find the height of the tree, we need to use trigonometry. The given angle of elevation (angle between the line of sight from the top of the tree to the top of the tower and the horizontal line) is 36 degrees.
Let's call the height of the tree "h."
We can use the tangent function to find the height of the tree.
tangent(angle) = opposite/adjacent
In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the tower.
tan(36 degrees) = h/44
To solve for "h," we rearrange the equation:
h = 44 * tan(36 degrees)
Now, let's calculate the height of the tree using a calculator:
h ≈ 44 * tan(36 degrees)
h ≈ 44 * 0.7265
h ≈ 32.00
Therefore, the height of the tree is approximately 32 meters.