The length of a trees shadow is 20 feet when the angle of elevation to the sun is 40 how tall is the tree

To find the height of the tree, we can use trigonometry, specifically 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 to the adjacent side. In this case, the tree height (which we are trying to find) is the opposite side of the angle of elevation, and the length of the shadow is the adjacent side.

Let's denote the height of the tree as "h." According to the tangent function:

tan(angle) = opposite / adjacent

Given that the angle of elevation is 40 degrees, we can write:

tan(40°) = h / 20 feet

To solve for "h," multiply both sides by 20 feet:

h = 20 feet * tan(40°)

Now, we can use a calculator to find the value of tan(40°) and then multiply by 20 to find the height of the tree.

Using a scientific calculator, we find:

tan(40°) ≈ 0.8391 (rounded to four decimal places)

So:

h ≈ 20 feet * 0.8391 h ≈ 16.782 feet

Therefore, the approximate height of the tree is 16.78 feet.