(50 points) An aerial photograph is taken of a building. The photograph is taken when the angle of elevation of the sun is 25 degrees. The shadow is determined to be 80 feet long. How tall is the building?

To determine the height of the building using the length of its shadow and the angle of elevation of the sun, we can use trigonometric ratios. For this situation, the tangent ratio is most appropriate.

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

 Here's the formula: tan(θ) = opposite / adjacent

In our case, the angle of elevation (θ) is 25 degrees, "opposite" would be the height of the building (which we're trying to find), and "adjacent" is the length of the shadow (80 feet).

Let's call the height of the building "h". Therefore: tan(25°) = h / 80

Now solve for "h": h = 80 * tan(25°)

First, calculate the tangent of 25 degrees using a calculator: tan(25°) ≈ 0.4663

Now, multiply this by 80 feet to find the height of the building: h ≈ 80 * 0.4663 ≈ 37.304

So the building is approximately 37.30 feet tall.