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Video: Finding the Unknown Lengths in a Right-Angled Triangle Using Pythagoras’s Theorem

Kathryn Kingham

Given that the triangle 𝐴𝐵𝐶 is right-angled at 𝐵, 𝐴𝐵 = 12 cm, and 𝐵𝐶 = 5 cm, find the length of the line segment 𝐴𝐶.


Video Transcript

Given that the triangle 𝐴𝐵𝐶 is right-angled at 𝐵, and 𝐴𝐵 equals 12 centimeters 𝐵𝐶 equals five centimeters, find the length of 𝐴𝐶.

Firstly, we can go ahead it and sketch our triangle. Our problem told us that it was right-angled that angle 𝐵. We label the 𝐵 as a right angle and then label the other two points 𝐴 and 𝐶. 𝐴𝐵 is 12 centimeters long, so we want to label that distance. 𝐸𝐶 is five centimeters long, and we’re trying to find the value of 𝐴𝐶.

We don’t know that distance; that’s what we’re looking for. And what we need now is the Pythagorean theorem; it says if you square the shortest two sides and add them together, they will be equal to the square of the longest side of any right triangle.

But most of the time we just say a squared plus b squared equals d squared. In our case, a would be equal to five centimeters, b would be equal to 12 centimeters, and c is our missing value. So we plug the information we know into our formula: five squared is 25; 12 squared is 144; and when we add those together, we’ll get 𝐶 squared; 25 plus 144 equals 169.

Remember that were not looking for the value of c squared; we’re only looking for the value of c, which means we need to take the square root of c squared. And the square root of 169—the square root of c squared equals c—the square root of 169 is 13.

The distance from 𝐴 to 𝐶, the length of side 𝐴𝐶, equals 13 centimeters.