Johns eyes are 6 ft from the ground. He is standing 70 ft away from a tree. If the angle of elevation is 24 degrees, then how tall is the tree?
draw a diagram. It is clear that
tan 24° = (h-6)/70
To find the height of the tree, we can use the trigonometric concept of tangent function.
Let's draw a right triangle where the tree is positioned at the top vertex and John's eyes are at the bottom vertex, forming a right angle.
The height of the tree can be represented as the opposite side, and John's distance from the tree can be represented as the adjacent side. We know the angle of elevation, which is 24 degrees.
Now, we can use the tangent function to find the height of the tree.
Tangent of an angle equals the opposite side divided by the adjacent side.
Tan(24 degrees) = Opposite / Adjacent
Tan(24 degrees) = Height of the tree / 70 ft
To isolate the height, we can rearrange the equation:
Height of the tree = Tan(24 degrees) * 70 ft
Now we can calculate the height:
Height of the tree ≈ Tan(24 degrees) * 70 ft
Using a scientific calculator or a trigonometric table, we can find that Tan(24 degrees) is approximately 0.44504187.
Therefore, the height of the tree is approximately:
Height of the tree ≈ 0.44504187 * 70 ft
Height of the tree ≈ 31.15 ft
So, the tree is approximately 31.15 ft tall.