On an inclined road, which makes an angle of 25 degrees with the horizontal plane, stands a vertical tower. At a point Q, 150 ft from the base of the tower down the road, the angle of elevation to the top of the tower is 65. How high is the tower?

as usual, draw a diagram, and you will see that

(h + 150*sin25°)/(150*cos25°) = tan65°

To find the height of the tower, we can use trigonometry. Let's break down the problem:

1. Draw a diagram: Start by drawing a diagram of the situation. The tower is vertical, and the road is inclined at a 25-degree angle with respect to the horizontal plane.

|\
Q | \ Tower
| \
-----
Road

2. Identify the known values: From the problem, we know that the angle of elevation to the top of the tower from point Q is 65 degrees, and the distance from the base of the tower to point Q along the road is 150 ft.

3. Identify the trigonometric function: In this case, we are given the angle of elevation and the opposite side length (the height of the tower). We need to use the tangent function, which is defined as the opposite side divided by the adjacent side.

4. Set up the equation: Using the tangent function, we have:

tan(65 degrees) = height of the tower / 150 ft

5. Calculate the height of the tower: Rearranging the equation, we have:

height of the tower = tan(65 degrees) * 150 ft

Using a calculator, we find:

height of the tower ≈ tan(65 degrees) * 150 ft ≈ 332.15 ft

Therefore, the height of the tower is approximately 332.15 ft.