## rebeccaskell94 Group Title 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 2 years ago 2 years ago

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2. ParthKohli Group Title

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

yes.

4. ParthKohli Group Title

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 Group Title

Hmm. No...

7. ParthKohli Group Title

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 Group Title

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 Group Title

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12. ParthKohli Group Title

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 Group Title

Yep!

256 or √16?

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

17. ParthKohli Group Title

Umm...no.....

18. ParthKohli Group Title

What is $$16^2$$?

oh duhhrr give me a sec

512=c^2 or c=22.6?

21. ParthKohli Group Title

-___- √512 ? maybe?

23. ParthKohli Group Title

Yep, but you have to simplify that radical.

Or! 16√2 ?

25. ParthKohli Group Title

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 Group Title

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 Group Title

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 Group Title

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

Okay!

33. ParthKohli Group Title

Wanna know it for 30-60-90 too?