A Man 1.5m tall observe That The Angle Of Elevation Of The Top Of a Building 24m away Is 41°.hat Is The Height Of The Building Correct To 3 significant Figures
To find the height of the building, we can use the tangent function to relate the angle of elevation and the height. Here's how:
1. Draw a diagram: Draw a triangle to represent the situation. Label the height of the building as 'h', the distance from the observer to the building as '24m', and the angle of elevation as 41°. The observer's eye level is 1.5m above the ground.
2. Identify the right triangle: In the diagram, the height of the building (h) is the vertical leg of the right triangle, and the observer's line of sight to the top of the building is the hypotenuse.
3. Use the tangent function: The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the observer to the building (24m).
So, we have:
tan(θ) = h / 24m
Rearrange the formula to solve for h:
h = 24m * tan(θ)
Substitute the values:
h = 24m * tan(41°)
4. Calculate the height: Use a scientific calculator or any calculator that has trigonometric functions to find the tangent of 41°. Multiply this value by 24m to get the height of the building.
h ≈ 24m * tan(41°)
h ≈ 24m * 0.869
h ≈ 20.9m
Thus, the height of the building, correct to 3 significant figures, is approximately 20.9 meters.