The angle of elevation of the sun is 27 degree. If a tree is 12 yd tall how long will the shadow be?
I got 13.5.
i want to know how tall the tree is not the shadow
I guess the shadow is 12 yards = 36 feet long ?
if so
tan 27 = height/36
height = 36 tan 27 feet high
=36 * .51 feet or about 18 feet or 6 yards tall
To calculate the length of the shadow cast by the tree, we can use the concept of trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation (in this case, 27 degrees) to the length of the shadow and the height of the tree.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this scenario, the height of the tree is the opposite side, and the length of the shadow is the adjacent side.
Let's use the following variables:
- Angle of elevation of the sun: θ = 27 degrees
- Height of the tree: h = 12 yards
- Length of the shadow: x (to be calculated)
Now, we can set up the equation using the tangent function:
tan(θ) = h / x
Plugging in the given values:
tan(27 degrees) = 12 / x
To solve for x, we need to isolate it. We can rewrite the equation as:
x = 12 / tan(27 degrees)
Now, we can calculate the value of x using a calculator or by applying the tangent function to 27 degrees.
Using a calculator, tan(27 degrees) is approximately 0.5095.
So,
x = 12 / 0.5095
x ≈ 23.51 yards
Therefore, the length of the shadow cast by the tree is approximately 23.51 yards.