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
Study your basic trig ratios.
height/42 = tan 36°
height = .....
To find the height of the tower, we can use trigonometry. In this case, we have the angle of elevation, which is the angle formed between the ground and the line of sight from the observer to the top of the tower.
The tangent function can help us find the height of the tower. The formula is as follows:
tangent(angle) = opposite/adjacent
In this case, the angle is 36 degrees, the opposite side is the height of the tower, and the adjacent side is the 42m distance from the base of the tower to the observer.
So, we can set up the equation as follows:
tan(36 degrees) = height/42m
Now, we need to solve for the height. We can do this by rearranging the equation:
height = tan(36 degrees) * 42m
Using a calculator, we can find the value of tan(36 degrees), which is approximately 0.7265. Plugging in this value into the equation, we get:
height = 0.7265 * 42m
Calculating this, we find:
height ≈ 30.48m
Therefore, the height of the tower is approximately 30.48 meters.