From a point P situated on level ground, the angle of elevation to the top of a vertical tower is 30°. If the height of the tower is 100 meters, what is the distance from point P to the base of the tower?

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Accepted Answer

To find the distance from point P to the foot of the tower, we need to apply trigonometric concepts.

Let's denote the tower as AB where A is the base and B is the top. Point P is on the ground, and we need to find the distance AP.

Since the angle of elevation from P to B is 30°, we have angle APB = 30°. The height of the tower AB = 100 m.

In the right-angled triangle APB, we can establish the relationship between the height and the distance using tangent:

tan 30° = AB/AP

We know that tan 30° = 1/√3

Therefore, AB/AP = 1/√3

Rearranging to find AP:
AP = AB × √3 = 100 × √3 meters

Using the approximate value of √3 ≈ 1.73:
AP = 100 × 1.73 = 173 meters

Therefore, the distance from point P to the foot of the tower is 173 meters.

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