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You are standing on the corner of a square whose side length is 25 feet. Standing on the opposite corner from you is a tall tree. The angle of elevation from your position to the top of the tree is exactly 60°. How tall is the tree?
- a)25√ 2
- b)25√ 3
- c)25√ 6
- d)50√ 3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
You are standing on the corner of a square whose side length is 25 fee...
First find the distance of the diagonal d along the ground from corner to corner. Using Pythagorean theorem with sides 25 and 25, we get:
252 + 252 = d2
2 × 252 = d2
d = 25√ 2 .
Then to obtain the height h of the tree, use the tangent ratio with angle 60°.
tan 60° = x / (25√ 2 )
√ 3 = x / (25√ 2 )
x = 25√ 2 × √ 3 = 25√ 6
Most Upvoted Answer
You are standing on the corner of a square whose side length is 25 fee...
Degrees. How tall is the tree?
To solve this problem, we can use trigonometry and the properties of a right triangle. First, we can draw a diagram:
```
A
/|
/ |
/ | h
/ |
----B----
25 ft.
```
In this diagram, A represents the top of the tree, B represents your position, and h represents the height of the tree. The angle of elevation from your position to the top of the tree is 60 degrees.
Next, we can use the tangent function to find the value of h:
```
tan(60 degrees) = h / 25 ft.
```
We can simplify this equation:
```
tan(60 degrees) = sqrt(3)
h / 25 ft. = sqrt(3)
h = 25 ft. * sqrt(3)
h ≈ 43.3 ft.
```
Therefore, the tree is approximately 43.3 feet tall.
To solve this problem, we can use trigonometry and the properties of a right triangle. First, we can draw a diagram:
```
A
/|
/ |
/ | h
/ |
----B----
25 ft.
```
In this diagram, A represents the top of the tree, B represents your position, and h represents the height of the tree. The angle of elevation from your position to the top of the tree is 60 degrees.
Next, we can use the tangent function to find the value of h:
```
tan(60 degrees) = h / 25 ft.
```
We can simplify this equation:
```
tan(60 degrees) = sqrt(3)
h / 25 ft. = sqrt(3)
h = 25 ft. * sqrt(3)
h ≈ 43.3 ft.
```
Therefore, the tree is approximately 43.3 feet tall.
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