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