### Video Transcript

In triangle π΄π΅πΆ, π΄π΅ squared plus π΅πΆ squared is less than π΄πΆ squared. What type of angle is π΅?

To solve this problem, we can actually use the Pythagorean theorem and actually use an adaptation of it to help us decide what type of angle π΅ is. Well, we know that π squared plus π squared equals π squared. But this is only the case if we have a right triangle. And thatβs a triangle with a right angle. And the right angle is opposite our π, which is our longest side.

And then we have the relationship which is that if π squared plus π squared is less than π squared, then actually weβre gonna have an obtuse triangle. And that means that the angle opposite our longest side is going to be obtuse.

And then finally, we have π squared plus π squared is greater than π squared. This actually shows us that itβs an acute triangle. So, weβre gonna have an acute angle opposite our π.

Okay, great! So we now have these three relationships that we can use. So letβs use them to help us decide what type of angle π΅ is in our triangle π΄π΅πΆ. To help us visualize the problem, Iβve actually just drawn a triangle. It doesnβt have to bear any resemblance to the triangle that we have. Itβs just to understand which side is opposite which angle.

So we can see that angle π΅ is opposite the side π΄πΆ. And as this is the case, we can now work out what type of angle angle π΅ is? Because, therefore, as π΄π΅ squared plus π΅πΆ squared is less than π΄πΆ squared, we can look at our second relationship and we can say that, in fact, itβs going to be an obtuse triangle. And therefore, we can say angle π΅ is obtuse.