You're about 20 meters away from a tall building, and you know your angle of elevation to the top of the building is 40 degrees. How tall is that building for real?
To determine the height of the building, we can use trigonometry. Specifically, we can use the tangent function, as it relates the angle of elevation to the height and distance.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the distance from your position to the building.
Let's proceed with the calculation:
1. Convert the angle of elevation from degrees to radians. Since most trigonometric functions expect values in radians, we need to convert 40 degrees to radians. We do this by multiplying the angle by π/180.
Angle in radians = 40 × π/180 = 0.698 radians (rounded)
2. Now, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the building divided by the distance.
tangent(0.698) = Height of the building / 20 meters
3. Rearrange the equation to solve for the height of the building.
Height of the building = tangent(0.698) × 20 meters
4. Calculate the height of the building using a calculator or computer:
Height of the building ≈ 0.839 × 20 ≈ 16.78 meters
Therefore, the height of the building is approximately 16.78 meters.
tan 40° = h/20
h = ...