Heights And Distances

To solve the problem, we need to find the angle of elevation of the sun when the length of the shadow of a vertical pole is times its height.

1. Understanding the Triangle Formed:
A right-angled triangle is formed by:
- The vertical pole (opposite side),
- The shadow (adjacent side),
- The line from the top of the pole to the tip of the shadow (hypotenuse).
Let the height of the pole be , then the length of the shadow is .

2. Using the Tangent Function:
The tangent of the angle of elevation is given by:

3. Finding the Angle:
We know that:

Therefore,

Final Answer:
The angle of elevation to the sun is 30°.