In right triangle ABC, m∠C = 90, AC = 7, and AB = 13. What is the length of BC?

Answer 1

Hi, Grace

To solve this problem, we'll need to use the Pythagorean Theorem. But, first let's state what we know.

There's a right triangle ABC - and we know that the angle ∠C is the right angle in that triangle, meaning that the side across from it, AB, will be the hypotenuse.

We also know the length of side AB is 13, and one of the legs AC is 7.

We need to find the length of side BC.

Well, the Pythagorean Theorem says that:

C² = A² + B²

Meaning that the square of a right triangle's hypotenuse is equal to the square of one of each of its legs.

So, let's replace these variables with the info for this problem.

The hypotenuse C is side AB, and the other two legs are AC and BC.

1. So let's rewrite C² = A² + B² as (AB)² = (AC)² + (BC)²
2. Now, substitute in the values that we do know:
3. (AB)² = (AC)² + (BC)² becomes (13)² = (7)² + (BC)²
4. And simplify: (13)² = (7)² + (BC)² becomes 169 = 49 + (BC)²

Now we just have to solve for the missing side length.

1. Subtract 49 from both sides.
2. 169 - 49 = 49 + (BC)² - 49 becomes 120 = (BC)²
3. Now take the square root of each side.
4. √120 = √(BC)² becomes 2√30 = BC

And, there you have the side length of BC.

Hope this helps!

Daniel