The angle of elevation to the top of a tower is 27 degrees, taken from a point 19 meters from the base of the tower. How high is the tower?
TanTheta=h/19
solve for h.
To find the height of the tower, we can use trigonometry and apply the tangent function.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the angle of elevation is 27 degrees, and the adjacent side is the distance from the base of the tower to the point of observation (19 meters).
So, we have:
tangent(27°) = opposite side / 19 meters
Now, we can solve for the height of the tower (opposite side):
opposite side = tangent(27°) * 19 meters
Using a scientific calculator or an online calculator, we can calculate the tangent of 27°:
tangent(27°) ≈ 0.5095
Now we substitute this value into the equation:
opposite side ≈ 0.5095 * 19 meters
opposite side ≈ 9.691 meters
Therefore, the height of the tower is approximately 9.691 meters.