The angle of depression from the top of a building to a point P on the ground is $23.6^{\circ}$. The distance from P to the foot of the building is 50 m. We need to calculate the height of the building, correct to the nearest meter.

1. Problem Description

The angle of depression from the top of a building to a point P on the ground is $23.6^{\circ}$. The distance from P to the foot of the building is 50 m. We need to calculate the height of the building, correct to the nearest meter.

2. Solution Steps

Let $h$ be the height of the building. The angle of depression from the top of the building to point P is the same as the angle of elevation from point P to the top of the building.

Therefore, we have a right triangle where the angle of elevation is $23.6^{\circ}$, the adjacent side is 50 m, and the opposite side is $h$. We can use the tangent function to relate these values:

$tan(\theta) = \frac{opposite}{adjacent}$

In our case, $\theta = 23.6^{\circ}$, the opposite side is $h$, and the adjacent side is 50 m.

So we have:

$tan(23.6^{\circ}) = \frac{h}{50}$

To find the height $h$, we multiply both sides of the equation by 50:

$h = 50 * tan(23.6^{\circ})$

Now we calculate the value of $tan(23.6^{\circ})$:

$tan(23.6^{\circ}) \approx 0.43697$

Then we calculate the height:

$h = 50 * 0.43697 \approx 21.8485$

We need to round the height to the nearest metre.

$h \approx 22$ m

3. Final Answer

The height of the building is approximately 22 meters.