The angle of elevation of the top of a tower from a point 42m away from its base on level ground is 36°. Find the height of the tower
To find the height of the tower, we can use trigonometry. We can consider the given information as a right triangle, with the tower being the vertical side, the distance from the base to the point of observation being the horizontal side, and the line of sight as the hypotenuse.
Let's break down the problem into components:
1. The angle of elevation is given as 36°.
2. The distance from the base to the point of observation is given as 42m.
Now, we can use trigonometry to find the height of the tower. In a right triangle, the tangent of an angle is equal to the ratio of the side opposite the angle to the side adjacent to the angle.
In this case, the tangent of the angle of elevation is equal to the height of the tower divided by the distance from the base to the point of observation.
So, using the formula:
tan(angle) = height / distance
Plugging in the given values:
tan(36°) = height / 42m
Now, we can solve for the height by multiplying both sides by 42m:
height = tan(36°) * 42m
Using a calculator, we can find that the approximate value of the tangent of 36° is 0.7265. Multiplying this by 42m, we get:
height ≈ 0.7265 * 42m
So, the height of the tower is approximately 30.51m.