At a certain time of the day the elevation of the sun is 40 degrees. To the nearest foot, find the height of a tree whose shadow is 35 feet long.
h/35 = tan40
To find the height of the tree, you can use the concept of similar triangles. The relationship between the height of the tree and the length of its shadow can be represented by the tangent of the angle of elevation of the sun.
First, we need to calculate the tangent of the angle of elevation.
Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the tree (which we want to find), and the adjacent side is the length of the shadow (35 feet).
So, the tangent of the angle of elevation is:
tan(40 degrees) = height of tree / length of shadow
Next, we can rearrange the equation to solve for the height of the tree:
height of tree = tan(40 degrees) * length of shadow
Now, let's plug in the values and calculate:
tan(40 degrees) ≈ 0.839
height of tree = 0.839 * 35 feet
height of tree ≈ 29.37 feet
Therefore, the height of the tree is approximately 29.37 feet.