A six-feet tall person wants to know the height of a tree. The person stands 20 feet from the tree and sights to the top of the tree. The angle of the sight line is 30 degrees. How tall is the tree?
Are we assuming the tree and person are on flat horizontal ground? If so, then
height=6+20tan30
Draw the figure, and verify that.
To determine the height of the tree, we can use the concept of trigonometry. Specifically, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this scenario, the person's line of sight forms a right triangle with the height of the tree as the opposite side, the distance from the person to the tree as the adjacent side, and the angle of elevation as one of the angles.
Given that the person is 6 feet tall and stands 20 feet away, and the angle of elevation is 30 degrees, we can set up the equation as follows:
tan(30 degrees) = height of tree / 20 feet
To solve for the height of the tree, we can rearrange the equation:
height of tree = 20 feet * tan(30 degrees)
Now, let's calculate the height of the tree using a scientific calculator or an online trigonometry calculator:
height of tree ≈ 20 feet * 0.577
height of tree ≈ 11.54 feet
Therefore, the height of the tree is approximately 11.54 feet.