Question Video: Identifying the Type of an Angle in a Triangle Using the Triangle Inequality Theorem | Nagwa Question Video: Identifying the Type of an Angle in a Triangle Using the Triangle Inequality Theorem | Nagwa

# Question Video: Identifying the Type of an Angle in a Triangle Using the Triangle Inequality Theorem Mathematics • Second Year of Preparatory School

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In triangle π΄π΅πΆ, (π΄π΅)Β² + (π΅πΆ)Β² < (π΄πΆ)Β². What type of angle is π΅?

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### Video Transcript

In triangle π΄π΅πΆ, π΄π΅ squared plus π΅πΆ squared is less than π΄πΆ 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 thatβs 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 weβre 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 itβs an acute triangle. So, weβre gonna have an acute angle opposite our π.

Okay, great! So we now have these three relationships that we can use. So letβs use them to help us decide what type of angle π΅ is in our triangle π΄π΅πΆ. To help us visualize the problem, Iβve actually just drawn a triangle. It doesnβt have to bear any resemblance to the triangle that we have. Itβs just to understand which side is opposite which angle.

So we can see that angle π΅ is opposite the side π΄πΆ. 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΅πΆ squared is less than π΄πΆ squared, we can look at our second relationship and we can say that, in fact, itβs going to be an obtuse triangle. And therefore, we can say angle π΅ is obtuse.

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