A vertical tower is on a 12° slope. from a 50 m down the hill, the angle of elevation of the top of the tower is 30°. find the height of the tower
To find the height of the tower, we can use trigonometric ratios in the given right triangle.
Let's first draw a diagram to visualize the situation. The vertical tower is on a 12° slope, and we have a right triangle formed by the tower, the slope, and the line of sight from the bottom of the hill to the top of the tower.
/|
/ |
h / | 30°
/ |
/____|
50 m
In this triangle, the side opposite the 30° angle represents the height of the tower (h), and the side adjacent to the 30° angle represents the distance along the slope (50 m).
We know that the tangent (tan) function is the ratio of the opposite side to the adjacent side in a right triangle. So, we can set up the following equation:
tan(30°) = h / 50
We can now solve for h by rearranging the equation and substituting the value for tan(30°):
h = 50 * tan(30°)
Now, let's calculate the height of the tower:
h = 50 * tan(30°)
≈ 29.0 meters
Therefore, the height of the tower is approximately 29.0 meters.