rebeccaskell94
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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rebeccaskell94
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|dw:1343141784834:dw|
ParthKohli
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All right. You do observe that this is a 45-45-90 which has a leg 16 right?
rebeccaskell94
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yes.
ParthKohli
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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?
rebeccaskell94
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Right triangle?
ParthKohli
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Hmm. No...
ParthKohli
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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.
rebeccaskell94
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oh lol xD
okay so it's isosceles
sorry D:
ParthKohli
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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).
rebeccaskell94
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So ST is 16 as well?
ParthKohli
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|dw:1343142127177:dw|
ParthKohli
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Yes! You got it! Now can you use the Pythagorean Theorem? :)
rebeccaskell94
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16^2 + 16^2 = c^2?
C in this case being RT?
ParthKohli
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Yep!
rebeccaskell94
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256 or √16?
rebeccaskell94
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I don't think I did that right...
ParthKohli
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Umm...no.....
ParthKohli
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What is \(16^2\)?
rebeccaskell94
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oh duhhrr give me a sec
rebeccaskell94
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512=c^2 or c=22.6?
ParthKohli
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It asks for the radical form :P
rebeccaskell94
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-___- √512 ? maybe?
ParthKohli
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Yep, but you have to simplify that radical.
rebeccaskell94
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Or! 16√2 ?
ParthKohli
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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!
rebeccaskell94
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Okay :D
ParthKohli
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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 \(1281283283283249483483 \sqrt2\)
rebeccaskell94
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D: That is genius
ParthKohli
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And, for example, if the hypotenuse is \(\pi\sqrt2\), then the leg is \(\pi\). Remember, you just remove that \(\sqrt2\) in the case of \(hypotenuse \Longrightarrow leg \).
rebeccaskell94
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*takes notes*
ParthKohli
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But remember, this method is \(\textbf{only for the 45-45-90 triangles}\).
rebeccaskell94
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Okay!
ParthKohli
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Wanna know it for 30-60-90 too?
rebeccaskell94
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Yeah! But I have to go make lunch for my siblings :( I'll be back in like 10-15 minutes :D
ParthKohli
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All right! :)