### Video Transcript

In triangle π΄π΅πΆ, suppose that π΄π΅ squared plus π΅πΆ squared equals 72.25 and π΄πΆ equals 8.5, what kind of angle is angle π΅? Option A, right. Option B, obtuse. Option C, acute.

Letβs start this question by drawing a diagram of our triangle π΄π΅πΆ. In the question, we can see the notation π΄π΅ squared plus π΅πΆ squared. And this might remind us of a special type of theorem, the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares on the other two sides. The Pythagorean theorem applies to right triangles only.

We can write an equation in the Pythagorean theorem for a triangle of lengths π, π and a hypotenuse π. And that is, that π squared equals π squared plus π squared. So in our diagram, if we have a right angle at angle π΅, then we could say that π΄π΅ squared plus π΅πΆ squared would be equal to the hypotenuse π΄πΆ squared.

So now, we need to work out if π΄π΅ squared plus π΅πΆ squared does actually equal π΄πΆ squared. Weβre given in the question that π΄π΅ squared plus π΅πΆ squared equals 72.25. And weβre told that the length π΄πΆ is equal to 8.5. So now, we establish if 72.25 equals 8.5 squared. And since we can evaluate that 8.5 squared equals 72.25, then we can say that π΄π΅ squared plus π΅πΆ squared does equal π΄πΆ squared. This means that the type of angle for angle π΅ is a right angle.