a tree casts a shadow that is 20 feet long. the angle of elevation from the end of the shadow to the top of the tree is 66 degrees. Determine the height of the tree to the nearest foot.
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To determine the height of the tree, we can use trigonometry. Let's break down the given information:
- The length of the shadow is 20 feet.
- The angle of elevation from the end of the shadow to the top of the tree is 66 degrees.
We can use the tangent ratio to solve this problem. The tangent of an angle is the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow. We can set up the equation as:
tan(66 degrees) = height of the tree / length of the shadow
Now, let's solve for the height of the tree:
height of the tree = tan(66 degrees) * length of the shadow
Using a calculator, we can find the tangent of 66 degrees:
tan(66 degrees) ≈ 2.030
Now, plug in the values:
height of the tree = 2.030 * 20 feet
height of the tree ≈ 40.6 feet
Therefore, the height of the tree is approximately 40.6 feet to the nearest foot.