A tree casts a shadow that is 18 feet in length. If the angle of elevation is 28 degrees, which of the following best represents the height of the tree?

To find the height of the tree, we can use trigonometry, particularly the tangent function, because we have the angle of elevation and the length of the shadow. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree in this case) to the adjacent side (length of the shadow).

Let's call the height of the tree "h" and the length of the shadow "l". According to the problem, "l" is 18 feet and the angle of elevation is 28 degrees. The tangent function can be written as:

tan(angle) = opposite / adjacent

So, for the given angle of 28 degrees, we have:

tan(28 degrees) = h / 18 feet

To find the height "h", we multiply both sides by 18 feet:

h = 18 feet * tan(28 degrees)

Now you would use a calculator to find the tangent of 28 degrees. Make sure the calculator is set to degrees if it has the ability to switch between degrees and radians.

Assuming the tangent of 28 degrees is approximately 0.5317 (you would want to use the exact value from your calculator for the most accurate answer),

h = 18 feet * 0.5317

h ≈ 18 feet * 0.5317 h ≈ 9.5706 feet

Thus, the height of the tree is approximately 9.57 feet.