orWatch a videoMitch is fishing from a small boat. A fish swimming at the same depth as the hook at the end of his fishing line is 5 meters away from the hook. If Mitch is 13 meters away from the fish, how far below Mitch is the hook?
Question
orWatch a videoMitch is fishing from a small boat. A fish swimming at the same depth as the hook at the end of his fishing line is 5 meters away from the hook. If Mitch is 13 meters away from the fish, how far below Mitch is the hook?
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we can consider the distance from Mitch to the fish as the hypotenuse, the distance from the fish to the hook as one side of the triangle, and the depth of the hook as the other side.
Given:
- The distance from Mitch to the fish (hypotenuse) is 13 meters.
- The distance from the fish to the hook is 5 meters.
We need to find the depth of the hook, which we'll call d.
According to the Pythagorean theorem:
13^2 = 5^2 + d^2
Solving for d, we get:
d^2 = 13^2 - 5^2 d^2 = 169 - 25 d^2 = 144
Taking the square root of both sides, we find that d = 12.
So, the hook is 12 meters below Mitch.
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