Finding side lengths of triangles
About this video
The video uses the Pythagorean theorem to pick which equations relate the sides k, v and t of a right triangle. Since t is the hypotenuse (the longest side, opposite the right angle), the correct equations are v^2 + k^2 = t^2 written in any equivalent order, while v^2 = t^2 + k^2 and an equation without squares are wrong.
You'll be able to
- identify the hypotenuse as the longest side, opposite the right angle.
- write the Pythagorean theorem for a right triangle using its own side labels.
- recognise equivalent forms of the Pythagorean theorem and reject incorrect ones.
Key words
- right triangle
- A triangle with one 90-degree angle.
- hypotenuse
- The longest side of a right triangle; it is opposite the right angle.
- Pythagorean theorem
- In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the other two sides.
Transcript
- [Narrator] Sides k, v, and t represent the lengths of the three sides of a right triangle, all right? Which equations represent the relationship between k, v, and t? And we're supposed to pick two answers. So pause this video, have a go at that. Okay, when we're dealing with a right triangle, we can see this is a right triangle, this is a 90-degree angle.
And we're thinking about the sides of a right triangle and the relationship between them, which should come to your mind as the Pythagorean theorem. And you might be familiar with Pythagorean theorem as a squared, as, whoops, as a squared plus b squared equals c squared, and that is indeed the Pythagorean theorem, but we need to remember what these a, bs and cs mean.
So the c right over here, not c squared, I'm just going to refer to the c right over here. This is referring to the length of the hypotonus, hypotonus, which is the longest side, longest side. It's also the side that is opposite the right angle. So in this case, c is t. This is t.
Now a and b are the other two sides. And you could pick either one to be a, and you could pick either one to be v. Oh, sorry, either one to be b. So for example, we could say that v is a and k is b, or vice versa. It doesn't make a difference because you could swap the order of these two.
Let me actually, you could swap the order of addition, but let's just go with that way. So if we just apply the Pythagorean theorem here, we would get v squared for a squared plus k squared for b squared is equal to... Let me write that a little bit neater. Whoops, my pen tablet's acting up.
K squared is equal to t squared, the hypotenuse squared, the longest side squared. So let's see. V squared plus k squared is equal to t squared. This one says k squared plus v squared is equal to t squared. Well, what we have here on the left is equivalent to what we have here.
It doesn't matter if we take v squared plus k squared or K squared plus v squared. Addition, you can do in either order. It's going to be the same thing. So I like this choice. This one says v squared is equal to t squared plus k squared. Now that's not right.
We could subtract k squared from both sides, but then we would get v squared is equal to t squared minus k squared. So I'll rule this one out. T squared is equal to v squared plus k squared. Yeah, this is, all that is, is what I wrote over here. We just swapped the two sides of the equality, which of course we know.
If the left is equal to the right, we could swap them around and just write t squared is equal to v squared plus k squared. So I like that choice as well. Now this last one, they forgot all the squares and we definitely can't make this claim. So we are done.
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