johns eyes are 6ft from the ground he is standing 70 ft away from a tree if the angle of evaluation is 24 degrees then how tall is the tree?
Review your basic trig functions. You will see that the height h can be found using
(h-6)/70 = tan 24°
To find the height of the tree, we can use trigonometry. Here's how you can calculate it:
Step 1: Draw a diagram to visualize the situation. Place John, the tree, and a vertical line representing the height of the tree.
Step 2: Identify the right triangle formed by John, the tree, and the vertical line.
Step 3: Label the known values on the diagram. Given that John's eyes are 6 ft from the ground and he is standing 70 ft away from the tree, label those values on the diagram.
Step 4: Identify the angle of elevation. In this case, it is given as 24 degrees. Label this angle on the diagram.
Step 5: Identify the side lengths of the right triangle based on the given information. The side opposite to the angle of evaluation (24 degrees) is the height of the tree we want to calculate.
Step 6: Use the tangent function to find the height of the tree. The tangent of an angle in a right triangle is equal to the ratio of the side opposite the angle to the side adjacent to the angle. In this case, we have the opposite side (height of the tree) and the adjacent side (70 ft).
So, calculate the tangent of 24 degrees: tan(24°) = opposite/adjacent = height/70.
Rearrange the equation to solve for the height: height = tan(24°) * 70.
Using a calculator, compute the tangent of 24 degrees, then multiply it by 70 to find the height of the tree.
The calculated height of the tree will be the answer to your question.