Video: Understanding the Definition of Right-Angled Triangles

In △𝐴𝐡𝐢, suppose that (𝐴𝐡)Β² + (𝐡𝐢)Β² = 72.25 and 𝐴𝐢 = 8.5 what kind of angle is ∠𝐡? [A] Right [B] Obtuse [C] Acute

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Video Transcript

In triangle 𝐴𝐡𝐢, suppose that 𝐴𝐡 squared plus 𝐡𝐢 squared equals 72.25 and 𝐴𝐢 equals 8.5, what kind of angle is angle 𝐡? Option A, right. Option B, obtuse. Option C, acute.

Let’s start this question by drawing a diagram of our triangle 𝐴𝐡𝐢. In the question, we can see the notation 𝐴𝐡 squared plus 𝐡𝐢 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‘Ž, 𝑏 and a hypotenuse 𝑐. And that is, that 𝑐 squared equals π‘Ž squared plus 𝑏 squared. So in our diagram, if we have a right angle at angle 𝐡, then we could say that 𝐴𝐡 squared plus 𝐡𝐢 squared would be equal to the hypotenuse 𝐴𝐢 squared.

So now, we need to work out if 𝐴𝐡 squared plus 𝐡𝐢 squared does actually equal 𝐴𝐢 squared. We’re given in the question that 𝐴𝐡 squared plus 𝐡𝐢 squared equals 72.25. And we’re told that the length 𝐴𝐢 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 𝐴𝐡 squared plus 𝐡𝐢 squared does equal 𝐴𝐢 squared. This means that the type of angle for angle 𝐡 is a right angle.

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