Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.) Round your answer to two places, where applicable.

Side AB Side BC Side AC

3
4
?

And since it is a Pythagorean Triple we know it is a 3,4, 5 triangle : )

AC^2 = AB^2 + BC^2

AC^2 = 3^2 +4^2
AC = 9 + 16
AC^2 = 25
AC = sq(25)
= 5

Well, well, well, we have a right triangle mystery on our hands! To solve this case, we'll have to put on our detective hats and use a little algebra.

In this right triangle, we have side AB with a length of 3 units, side BC with a length of 4 units, and side AC as the unknown hypotenuse. Let's call the length of side AC "x" for now.

Remember the famous Pythagorean theorem? It states that the square of the hypotenuse (side AC) is equal to the sum of the squares of the other two sides (AB and BC). Mathematically, we can express this as:

x^2 = 3^2 + 4^2

Calculating that equation, we get:

x^2 = 9 + 16
x^2 = 25

To find the length of side AC, we need to take the square root of 25:

x = √25 = 5

Therefore, the unknown side is 5 units long. Case solved, my friend!

To solve for the length of the unknown side, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (side AC) is equal to the sum of the squares of the lengths of the other two sides (sides AB and BC).

Here is how you can solve for the unknown side:

1. Identify the two sides given in the triangle:
- Side AB = 3.
- Side BC = 4.

2. Apply the Pythagorean theorem to solve for the unknown side:
- Use the formula: AC^2 = AB^2 + BC^2.
- Substitute the values: AC^2 = 3^2 + 4^2.

3. Calculate the squares:
- AC^2 = 9 + 16.
- AC^2 = 25.

4. Take the square root of both sides to find the length of side AC:
- AC = sqrt(25).
- AC = 5.

Therefore, the length of the unknown side AC in the right triangle is 5.

To solve for the length of the unknown side in the 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 (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC).

In this case, we have:

AB = 3
BC = 4

Let's substitute the given values into the equation and solve for the unknown length (denoted by "?"):

AC^2 = AB^2 + BC^2

AC^2 = 3^2 + 4^2
AC^2 = 9 + 16
AC^2 = 25

Now, we can take the square root of both sides to find the length of side AC:

AC = √25
AC = 5

Therefore, the length of the unknown side (AC) is 5.