A 12-foot tree casts a 22-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth.

To find the angle of elevation, we can use trigonometry. The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In this case, the height of the tree is the opposite side, and the length of the shadow is the adjacent side. We have the height of the tree (12 feet) and the length of the shadow (22 feet).

The formula for the tangent of an angle is:

tan(angle) = opposite / adjacent

Plugging in the values we have:

tan(angle) = 12 / 22 (opposite = 12 feet, adjacent = 22 feet)

Now, to find the angle, we need to take the inverse tangent (or arctan) of both sides of the equation:

angle = arctan(12 / 22)

Using a scientific calculator or an online calculator that has the arctan function, we find that:

angle ≈ 28.9 degrees

Therefore, the angle of elevation from the tip of the shadow to the top of the tree is approximately 28.9 degrees.

if the angle is x,

12/22 = tan(x)