Find the length of the missing leg of a right triangle given a leg of length 15 and a hypotenuse of length 17. Leave your answer in simplest radical form.
15^2 + b^2 = 17^2
225 + b^2 = 289
b^2 = 64
b = 8
ms. sue is correct! it’s 8😊
Thank you Ms. Sue!
Well, let's play a little game of "Find the Mystery Leg"! We have a right triangle with one leg measuring 15 units and the hypotenuse measuring 17 units. The missing leg wants to stay incognito and hide in the dark for a while. Let's call the mystery leg "x" for now.
Now, according to the Pythagorean theorem, the sum of the squares of the two legs is equal to the square of the hypotenuse. This sounds like a math crime scene investigation, doesn't it? Let's crack this case!
Using the Pythagorean theorem, we can set up the equation:
15^2 + x^2 = 17^2
Now, let's solve this equation and reveal the identity of our mysterious leg, shall we?
225 + x^2 = 289
To find x^2, we need to subtract 225 from both sides:
x^2 = 289 - 225
Guess what? x^2 is just itching to be unleashed from that cage:
x^2 = 64
Now, let's set x free by taking the square root of both sides:
x = √64
Congratulations! We found the missing leg! The length of the missing leg of the right triangle is √64, which simplifies to a lovely 8 units.
So, the length of the missing leg is 8 units. Mystery solved!
To find the length of the missing leg of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two legs.
Let's denote the missing leg as "x". We are given that one leg has a length of 15 and the hypotenuse has a length of 17. We can use the Pythagorean theorem to set up the equation:
x^2 + 15^2 = 17^2.
Simplifying this equation, we have:
x^2 + 225 = 289.
Subtracting 225 from both sides of the equation, we get:
x^2 = 289 - 225,
x^2 = 64.
To solve for x, we take the square root of both sides of the equation:
√(x^2) = √64,
x = ±√64.
Since we are looking for a positive length, we can take the positive square root of 64:
x = √64.
The square root of 64 is 8, so the missing leg of the right triangle has a length of 8.
Therefore, the length of the missing leg of the right triangle is 8.