I'm having problems with Pythagorean theorem: word problems. Please help me. Damon is fishing from a small boat. A fish swimming at the same depth as the hook at the end of his fishing line is 12 feet away from the hook. If Damon is 20 feet away from the fish, how far below Damon is the hook?
Thank you so much because I have been working on this for the past hour and I have gotten no where.
Reed? Reiny? Anyone? I'm not trying to rush anyone but I am really eager to find out what I've been doing wrong.
The hypotenuse is 20
one of the legs is 12
what is the other leg?
12^2 + x^2 = 20^2 = 400
x^2 = 400 - 144
x^2 = 256
x = 16
and yes, I am a fisherman.
By the way this is a 3, 4, 5 triangle
9 + 16 = 25
It's so clear now! Thank you so much! Are you seriously a fisherman though?
Yes, although not since I was a young man lobstering and ground fishing out of Gloucester, Massachusetts.
Sweet! I've never went fishing. The closest I've ever been to water is when I found a baby turtle near a river that I used to live by. Now I have three of them Tony, Tonia, and I still have to figure out if the last one is a girl or a boy. It's a challenge but that's what makes it fun!
To solve this Pythagorean Theorem word problem, we can use the formula a² + b² = c², where "a" and "b" are the two shorter sides of a right triangle, and "c" is the hypotenuse.
In this case, we have a right triangle formed by Damon, the fish, and the hook. The distance between the fish and the hook (12 feet) represents one side of the triangle, and the distance between Damon and the fish (20 feet) represents another side. We want to find the distance below Damon that the hook is located, which represents the remaining side of the triangle.
Let's denote the distance below Damon as "x." From the Pythagorean Theorem, we have:
x² + 12² = 20²
Simplifying this equation, we get:
x² + 144 = 400
Subtracting 144 from both sides, we have:
x² = 256
To solve for x, we take the square root of both sides:
√x² = √256
x = 16
Therefore, the hook is located 16 feet below Damon.
To apply the Pythagorean Theorem to word problems like this, you need to identify the right triangle, determine the lengths of the known sides, and then use the formula a² + b² = c² to find the missing side.