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Find the length of the missing side.

Mathematics
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@FutureMathProfessor Please help! Given reward if so!
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oh my goodness. lol.
\[a ^{2}+b ^{2}=c ^{2}\] \[8 ^{2}+15 ^{2}=x ^{2}\] \[64+225=x ^{2}\] \[x ^{2}=289\] \[x=\sqrt{289}\] \[x=17\]
@mitodoteira Can you please help with one more?
Okay
Aww that's not being a good sport.
The question didn't ask for x, should be 17^2 or 289
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Emily, what is the other question?
the length of the missing side would be what @arafatx mentioned. You can always plug it back in to the pythagorean identity to check your answer. a^2 +b^2 = c^2 (15)^2 + (8)^2 = (sqrt (289))^2 225 + 64 = 289
is that for the second one?
and for that question,you have a 45-45-90 triangle, therefore your proportions are 1:1:1*sqrt(2) By that i mean both of your base legs are the same and to find the hypotenuse you're going to multiply your base leg * sqrt(2)
b1 = 12, b2 = 12, hypotenuse = b1*sqrt(2)
Since
you guys are giving me 2 different answers. Which is it?
12*sqrt(2) is about equal to 17
@mitodoteira c^2 = a^2 + b^2 take x = 17, c=x (17)^2 = (12)^2 + (12)^2 289 = 288 nope.
That's because I'm rounding. The actual answer is irrational. If you look at my answer, I gave the answer to a few decimal places as well.
whereas we take c = 12sqrt(2) c^2= a^2 + b^2 (12sqrt(2))^2 = (12)^2 + (12)^2 288 = 288 You DO NOT round when finding lengths.
I gave the true answer, as well as the rounded one in case she needed it for something (I was often asked to give the answer to n decimal places instead of the exact answer).
the "true" answer is 12* sqrt(2) according to the 45-45-90 degree triangle.
Yes, it is. I don't see what the problem is.
Emily778 You've already chosen the best response. 0 In triangle ABC,
"if the answer is not an integer, leave it in simplest form" and therefore the simplest form is 12*sqrt(2)
What I said was 'x=12*sqrt(2), x APPROXIMATELY EQUALS 16.97056 approx 17' I am new to this community. Most others I have been to welcome extra information.
the approximation then would be longer than 16.97056. you'd have to include the whole number approximation, not rounding up to 17.
If it's suppose to be in exact or simplified form then leave it as radicals, fractions etc. If it asks for estimation, nearest number, or approximation then that's when you round up and change the radical to a number
so your final answer for the second problem should be left as a radical.
yeah, simplest form = \(12\sqrt{2}\)
Thank you Gane

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