When the angle of elevation of the sun from the ground is
25 degrees , how long is the shadow of a 20-foot light pole? Round your answer to the nearest tenth of a foot.
A diagram of a right-angle triangle. The angle of the right vertex is 25 degrees. The opposite side is the light pole, the adjacent side is shadow, and the hypotenuse side is extended up, named sunlight.
To find the length of the shadow, we can use the trigonometric function tangent (tan).
In the given right triangle, the angle of elevation is 25 degrees, and the side opposite the angle is the height of the pole, which is 20 feet.
Let's assume the length of the shadow is x feet.
According to the tangent function:
tan(angle) = opposite/adjacent
tan(25 degrees) = 20 feet / x
Using the tangent function, we can rearrange the equation to solve for x:
x = 20 feet / tan(25 degrees)
Using a calculator, we can find the value of tan(25 degrees) ≈ 0.4663.
x = 20 feet / 0.4663 ≈ 42.9 feet
Therefore, the length of the shadow of the 20-foot light pole is approximately 42.9 feet. Rounded to the nearest tenth of a foot, the length of the shadow is 42.9 feet.