## rebeccaskell94 3 years ago In △RST, what is the length of line segment RT? How old I'll draw it. Possible answers: 8 16 radical 2 32 16radical 3

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2. ParthKohli

All right. You do observe that this is a 45-45-90 which has a leg 16 right?

yes.

4. ParthKohli

Okay. Another thing that I should tell you—if two angles are equal, then two sides are equal too! Do you know what a triangle with two equal sides is known as?

Right triangle?

6. ParthKohli

Hmm. No...

7. ParthKohli

There are names given to the triangles based on their *sides*. Equilateral triangle - all sides equal. Isosceles triangle - two sides equal. Scalene triangle - no sides equal.

oh lol xD okay so it's isosceles sorry D:

9. ParthKohli

All right, so an isosceles triangle has 2 angles and 2 sides equal. So, we have TWO angles equal. This must be an isosceles triangle(which makes the two legs equal by default).

So ST is 16 as well?

11. ParthKohli

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12. ParthKohli

Yes! You got it! Now can you use the Pythagorean Theorem? :)

16^2 + 16^2 = c^2? C in this case being RT?

14. ParthKohli

Yep!

256 or √16?

I don't think I did that right...

17. ParthKohli

Umm...no.....

18. ParthKohli

What is $$16^2$$?

oh duhhrr give me a sec

512=c^2 or c=22.6?

21. ParthKohli

-___- √512 ? maybe?

23. ParthKohli

Yep, but you have to simplify that radical.

Or! 16√2 ?

25. ParthKohli

Yay! As you are done with the long method now, I'd give you a short-cut to do such questions involving a 45-45-90 triangle!

Okay :D

27. ParthKohli

If you are given a leg of a 45-45-90 triangle, you just put $$\sqrt2$$ in front of it to get the hypotenuse ^_^ • If the leg is $$8$$, then the hypotenuse is $$8\sqrt2$$ • If the leg is $$1281283283283249483483$$, then the hypotenuse is $$1281283283283249483483 \sqrt2$$

D: That is genius

29. ParthKohli

And, for example, if the hypotenuse is $$\pi\sqrt2$$, then the leg is $$\pi$$. Remember, you just remove that $$\sqrt2$$ in the case of $$hypotenuse \Longrightarrow leg$$.

*takes notes*

31. ParthKohli

But remember, this method is $$\textbf{only for the 45-45-90 triangles}$$.

Okay!

33. ParthKohli

Wanna know it for 30-60-90 too?

Yeah! But I have to go make lunch for my siblings :( I'll be back in like 10-15 minutes :D

35. ParthKohli

All right! :)