Video Transcript
In triangle πππ, ππ squared is greater than ππ squared minus ππ squared. What type of angle is π?
If we consider any triangle πππ, there are three possibilities for angle π. The first diagram shows that angle π is a right angle. The second diagram shows angle π is an acute angle, as it is less than 90 degrees or a right angle. In the third diagram, angle π is an obtuse angle, as it is greater than 90 degrees but less than 180 degrees. We need to consider the relationship between the lengths in the triangle, ππ, ππ, and ππ. In this question, we need to decide which triangle corresponds to the inequality ππ squared is greater than ππ squared minus ππ squared.
Pythagorasβ theorem states that in any right-angled triangle, π squared plus π squared is equal to π squared, where π is the length of the longest side known as the hypotenuse. This means that in our first diagram, ππ squared plus ππ squared is equal to ππ squared. As angle π gets smaller, the length ππ also gets smaller. This means that in the second diagram, the sum of the other two sides squared will be greater than ππ squared. Conversely, as angle π gets larger, the length ππ gets larger. This means that in our third diagram, ππ squared plus ππ squared is less than ππ squared.
We can now work out which of our three triangles matches the initial inequality. We can rule out the answer right angle as this has an equation and not an inequality. Letβs consider the initial inequality ππ squared is greater than ππ squared minus ππ squared. Adding ππ squared to both sides of this inequality gives us ππ squared plus ππ squared is greater than ππ squared. This corresponds to the second diagram. We can therefore conclude that, in this case, angle π is acute. It is less than 90 degrees.
