## anonymous 4 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

1. anonymous

|dw:1343141784834:dw|

2. ParthKohli

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

3. anonymous

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?

5. anonymous

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.

8. anonymous

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).

10. anonymous

So ST is 16 as well?

11. ParthKohli

|dw:1343142127177:dw|

12. ParthKohli

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

13. anonymous

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

14. ParthKohli

Yep!

15. anonymous

256 or √16?

16. anonymous

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

17. ParthKohli

Umm...no.....

18. ParthKohli

What is $$16^2$$?

19. anonymous

oh duhhrr give me a sec

20. anonymous

512=c^2 or c=22.6?

21. ParthKohli

22. anonymous

-___- √512 ? maybe?

23. ParthKohli

Yep, but you have to simplify that radical.

24. anonymous

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!

26. anonymous

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 $$1281283283283249483483 \sqrt2$$

28. anonymous

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 $$hypotenuse \Longrightarrow leg$$.

30. anonymous

*takes notes*

31. ParthKohli

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

32. anonymous

Okay!

33. ParthKohli

Wanna know it for 30-60-90 too?

34. anonymous

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! :)