A monkey is chained to a stake in the ground. The stake is 2.81 m from a vertical pole, and the chain is 3.61 m long. How high can the monkey climb up the pole?
Use Pythoragus' Theorem to solve this.
h^2=2.81^2+3.61^2
4.57m
To determine the height the monkey can climb up the pole, we need to use the concept of right triangles and the Pythagorean theorem.
Let's draw a diagram to help visualize the situation. The stake, pole, and chain form a right triangle. The stake and the pole form the two sides of the triangle, while the chain represents the hypotenuse.
```
Monkey
|
|
| Chain (3.61 m)
|
|
|
*-----------------*
| |
| Ground | Pole
| |
*-----------------*
(2.81 m)
```
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we can write the equation as:
a^2 + b^2 = c^2
Let's substitute the given values into the equation:
a^2 + 2.81^2 = 3.61^2
Simplifying this equation:
a^2 + 7.8961 = 13.0321
Subtracting 7.8961 from both sides:
a^2 = 13.0321 - 7.8961
a^2 = 5.136
Taking the square root of both sides:
a = √5.136
Calculating the square root:
a ≈ 2.2659
Therefore, the height that the monkey can climb up the pole is approximately 2.2659 meters.