To find the height of a tree, scientist Sally moves 160 feet away from the base of the tree and then, with a tool 6 feet tall, measures the angle of elevation to the top of the tree to be 62°. To the nearest foot, what is the height of the tree?
the bot is wrong again!!!!
basic trig problem:
height = 160tan62° = 300.9 ft
To find the height of the tree, we can use trigonometry and the angle of elevation provided.
1. Let's start by drawing a diagram to visualize the situation. The tree is represented as a vertical line, the distance from the tree to Sally is 160 feet, and the tool she's using is 6 feet tall.
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| \
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6ft \
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| \
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_____________________________
160ft
2. Now, we can use the tangent function to find the height of the tree. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree, and the adjacent side is the distance from Sally to the base of the tree.
tan(angle) = height of tree / distance to tree
tan(62°) = height of tree / 160
3. To solve for the height of the tree, we can rearrange the equation:
height of tree = tan(62°) * 160
4. Using a calculator, we can find the value of the tangent of 62°:
tan(62°) ≈ 1.8807
5. Now, we can calculate the height of the tree by multiplying this value by 160 feet:
height of tree ≈ 1.8807 * 160
height of tree ≈ 300.91 feet
6. Rounding to the nearest foot, the height of the tree is approximately 301 feet.
To find the height of the tree, we can use trigonometry. The angle of elevation and the distance between the observer and the base of the tree form a right triangle.
Here's how we can solve it step by step:
1. First, draw a diagram to visualize the problem. Label the base of the tree A, the top of the tree B, and Sally's position C.
```
B
/|
/ |
/ |
/ |h (height of the tree)
/ |
A/______|
160 ft C
```
2. Use the tangent function to relate the angle of elevation to the height of the tree. Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.
So, we can write the equation:
tan(62°) = h / 160 ft
3. Rearrange the equation to solve for h:
h = 160 ft * tan(62°)
4. Now, plug the values into a calculator to find the height of the tree:
h = 160 ft * tan(62°)
h ≈ 160 ft * 1.880726465 (rounded to 9 decimal places)
h ≈ 300.92 ft (rounded to two decimal places)
Therefore, the height of the tree, to the nearest foot, is approximately 301 feet.