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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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

Mathematics
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|dw:1343141784834:dw|
All right. You do observe that this is a 45-45-90 which has a leg 16 right?
yes.

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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?
Hmm. No...
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:
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?
|dw:1343142127177:dw|
Yes! You got it! Now can you use the Pythagorean Theorem? :)
16^2 + 16^2 = c^2? C in this case being RT?
Yep!
256 or √16?
I don't think I did that right...
Umm...no.....
What is \(16^2\)?
oh duhhrr give me a sec
512=c^2 or c=22.6?
It asks for the radical form :P
-___- √512 ? maybe?
Yep, but you have to simplify that radical.
Or! 16√2 ?
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
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
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*
But remember, this method is \(\textbf{only for the 45-45-90 triangles}\).
Okay!
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
All right! :)

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