From the top of a building the angle of depression of a point P on the ground is 15 degrees. The point P is 55 ft from the base of the building. Determine the height of the building.
h/55 = tan15°
To determine the height of the building, we can use trigonometry and the concept of right triangles. Here's how you can approach this problem:
Step 1: Draw a diagram:
Draw a right triangle with the building as the vertical side and the distance from the base of the building to point P on the ground as the horizontal side. Label the vertical side as 'h' (height of the building) and the horizontal side as '55 ft'.
Step 2: Identify relevant trigonometric ratios:
Since we are given the angle of depression (the angle between the line of sight from the top to the ground and the horizontal line), we can use the tangent ratio. In this case,
tangent(angle) = Opposite / Adjacent.
In our triangle, the tangent of the angle of depression of 15 degrees is equal to the height of the building divided by the horizontal distance from the base of the building to point P on the ground. Therefore,
tangent(15 degrees) = h / 55 ft.
Step 3: Solve for the height 'h':
To find the height of the building, we need to isolate 'h' in the equation above. To do that, we can rearrange the equation as follows:
tangent(15 degrees) = h / 55 ft
h = tangent(15 degrees) * 55 ft
Step 4: Calculate the height of the building:
Using a calculator, find the tangent of 15 degrees (approximately 0.267949). Multiply this value by 55 ft.
h ≈ 0.267949 * 55 ft
h ≈ 14.734 ft
Therefore, the height of the building is approximately 14.734 feet.