To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 35 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 37°. What is the height of the tower, to the nearest meter?
Draw a diagram and review your basic trig functions. It should be clear that
(h-2)/35 = tan37°
Now finish it off
To find the height of the tower, we can use trigonometry. We have a right triangle, where the height of the tower is the opposite side, the distance from the base of the tower to the transit is the adjacent side, and the angle of elevation is the angle opposite to the height.
First, let's label the sides of the triangle:
- The height of the tower is h.
- The distance from the base of the tower to the transit is d = 35 meters.
- The angle of elevation is θ = 37°.
We can use the tangent function to relate the height of the tower to the other sides of the triangle:
tan(θ) = opposite/adjacent
tan(37°) = h/35
Now, we solve the equation for h by multiplying both sides of the equation by 35:
h = 35 * tan(37°)
h ≈ 35 * 0.7536
h ≈ 26.38
Therefore, the height of the tower is approximately 26.38 meters. To the nearest meter, the height of the tower is 26 meters.