Answer:
34.22m
Explanation:
To find the height of the tree, we can use trigonometry. We have the distance from the base of the tree to the point where the angle of elevation is measured (38 meters) and the angle of elevation (42 degrees). We can use the tangent function to calculate the height.
Let's denote the height of the tree as "h."
In a right triangle formed by the base of the tree, the top of the tree, and the point where the angle of elevation is measured, the tangent of the angle of elevation is defined as the ratio of the opposite side (height of the tree, h) to the adjacent side (distance from the base to the point of measurement, 38 meters):
tan(42 degrees) = h / 38
To find the height, we can rearrange the equation:
h = 38 * tan(42 degrees)
Using a calculator, we can evaluate this expression:
h ≈ 38 * 0.9004
h ≈ 34.2152
Therefore, the height of the tree is approximately 34.22 meters.