The angle of elevation of the sun, when the length of the shadow of a tree sqrt(3) times the height of the tree, is:

The problem involves trigonometry, specifically the tangent of an angle in a right triangle.

Step 1: Understand the problem The problem states that the length of the shadow of a tree is sqrt(3) times the height of the tree. We are asked to find the angle of elevation of the sun.

Step 2: Draw a right triangle We can represent this situation with a right triangle, where the height of the tree is one side, the length of the shadow is the other side, and the angle of elevation is the angle we are trying to find.

Step 3: Use the tangent function In a right triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the tangent of the angle of elevation is equal to the height of the tree divided by the length of the shadow.

Step 4: Set up the equation We know that the length of the shadow is sqrt(3) times the height of the tree, so we can write the equation as follows:

tan(angle) = height / (sqrt(3) * height)

Step 5: Solve the equation The height of the tree cancels out, leaving us with:

tan(angle) = 1 / sqrt(3)

Step 6: Find the angle The angle whose tangent is 1/sqrt(3) is 30 degrees. Therefore, the angle of elevation of the sun is 30 degrees.