How tall is the tree if the sun is at a 53° angle above the horizon and the shadow is 8.0 meters long?

10.6

To determine the height of the tree, we can use the concept of trigonometry. We'll need to use the tangent function since we have the angle and the length of the shadow.

Let's assume "h" is the height of the tree and "s" is the length of the shadow. We also have the angle "θ" which is 53° in this case.

The tangent of an angle is the opposite side divided by the adjacent side. In our case, the opposite side is the height of the tree (h) and the adjacent side is the length of the shadow (s), so we can use the equation:

tan(θ) = h / s

Plugging in the values we have:

tan(53°) = h / 8.0

Now, we can rearrange the equation to solve for "h":

h = tan(53°) * 8.0

Using a scientific calculator or an online trigonometric calculator, we can find the tangent of 53°:

tan(53°) ≈ 1.327

Now, we can substitute the value back into the equation:

h ≈ 1.327 * 8.0

Calculating this, we find:

h ≈ 10.616 meters

Therefore, the height of the tree would be approximately 10.616 meters.