If your shadow is twice your height, what is the angle of elevation of the sun?

The angle of elevation of the sun can be found using trigonometry, specifically the tangent function.

Here are the steps:

1. Understand the problem: In this case, the shadow is twice the height of the person. This forms a right triangle where the height of the person is one side, the length of the shadow is the other side, and the angle we want to find is the angle between the ground and the line from the person to the sun.

2. Use the tangent function: In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the person and the adjacent side is the length of the shadow.

3. Set up the equation: tan(θ) = height / shadow = 1 / 2.

4. Solve for the angle: θ = arctan(1/2).

5. Use a calculator to find the arctan(1/2): θ ≈ 26.57 degrees.

So, the angle of elevation of the sun is approximately 26.57 degrees.