a 7 foot tall man is standing 65 feet away from a tower. if the angle of elevation is 35 degrees. what is the height of the tower to nearest tenth of a foot?

If there are h feet of tower above the man's eyes, h/65 = tan35°

so, the tower height is 7 + 65tan35° = 52.5 ft

To find the height of the tower, we can use basic trigonometry principles. We have a right triangle formed by the man, the tower, and the ground.

Let's consider the given information:
- The man's height is 7 feet.
- The distance between the man and the tower is 65 feet.
- The angle of elevation from the man to the top of the tower is 35 degrees.

To solve this problem, we'll focus on the side opposite the angle of elevation (the height of the tower) and the side adjacent to the angle of elevation (the distance between the man and the tower).

We know that the tangent function relates the opposite side (height of the tower) to the adjacent side (distance between the man and the tower).

We can use the tangent function as follows:
tan(angle) = height of the tower / distance to the tower

Plugging in the known values:
tan(35 degrees) = height of the tower / 65 feet

Now, we can solve for the height of the tower. Rearranging the equation, we get:
height of the tower = tan(35 degrees) * 65 feet

Calculating this expression, we find that the height of the tower is approximately 45.5 feet (rounded to the nearest tenth of a foot).