Helen stands 66 m away from the base of the tree. If the line of sight makes an angle of 30 with the top of the tree with respect to the horizon. What is the height (h) of the tree?
h/66= tan 30, right?
To find the height of the tree, we can use trigonometry.
Let's label the height of the tree as h and the distance from Helen to the tree as d (66 m in this case). The angle between the line of sight to the top of the tree and the horizon is 30 degrees.
Using the concept of trigonometry, we can use the tangent function to find the height of the tree. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the height of the tree is the opposite side, and the distance from Helen to the tree is the adjacent side.
So we have:
tan(30°) = h / d
Now we can rearrange the formula to solve for h:
h = d * tan(30°)
Substitute the value of d (66 m) into the formula:
h = 66 * tan(30°)
Using a calculator, we can evaluate the tangent of 30 degrees (approximately 0.5774):
h ≈ 66 * 0.5774
h ≈ 38.04
Therefore, the height of the tree is approximately 38.04 meters.