A 1.7-metre tall man stands 12 m from the base of a tree. He views the top of the tree at an angle of elevation of 58°. How tall is the tree?
Draw a diagram, and review your basic trig functions. It should be clear that
(h-1.7)/12 = tan58°
h = 20.9 m
To find the height of the tree, we can use the tangent function since we have the angle of elevation and the distance from the base of the tree.
1. First, let's write down the given information:
- The man's height: 1.7 meters.
- The distance from the man to the base of the tree: 12 meters.
- The angle of elevation: 58°.
2. Draw a diagram to visualize the problem. Label the man's height, the distance to the tree, and the unknown height of the tree.
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12 meters
3. Using the tangent function, we can write the equation:
tan(58°) = h / 12
4. Now, solve the equation for h (tree height):
h = 12 * tan(58°)
5. Calculate h using a calculator or by hand:
h ≈ 12 * 1.6643 ≈ 19.972 meters
Therefore, the tree is approximately 19.972 meters tall.
To find the height of the tree, we can use trigonometry.
Let's draw a diagram to visualize the problem.
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Man Tree
From the diagram, we can see that we have a right-angled triangle, with the height of the tree as the vertical side, the distance from the man to the tree as the horizontal side, and the line of sight from the man to the top of the tree as the hypotenuse.
We are given that the man's distance from the tree is 12 m, and the angle of elevation is 58°.
Now, let's define our trigonometric functions:
- In this case, since we are dealing with the angle of elevation, we can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In our case, the opposite side is the height of the tree, and the adjacent side is the distance from the man to the tree.
So, we have:
tan(58°) = height of the tree / 12 m
Now, we can rearrange the equation to solve for the height of the tree:
height of the tree = tan(58°) * 12 m
Calculating this expression, we can find the height of the tree:
height of the tree ≈ tan(58°) * 12 m
Using a scientific or graphing calculator, we can evaluate the expression:
height of the tree ≈ 1.61 * 12 m
height of the tree ≈ 19.32 m
Therefore, the height of the tree is approximately 19.32 meters.