Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem, and then find the values of the six trigonometric functions for angle B. Rationalize denominators when applicable. b = 8, c = 11

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Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem, and then find the values of the six trigonometric functions for angle B. Rationalize denominators when applicable. b = 8, c = 11

Mathematics
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For clarification, does the problem specify which sides b and c are? The length of the unknown side depends on whether it is a leg of the triangle or not.
it states that b is 8 and c is 11 and that C is on the right angle of the triangle which means that c is the hypotenuse.
Okay, so the Pythagorean theorem states that \[a^2+b^2=c^2\] If you rearrange it to find a, it would become \[a=\sqrt[2]{c^2-b^2}\]

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I'm going to guess that your triangle looks something like this, if that was how c was assigned: |dw:1327907085608:dw| The trigonometric functions are sin, cos, tan, csc, sec, and cot.
well there are 2 solutions to this a = hypotenuse the a^2 = 8^2 + 11^2 a = shorter side A^2 = 11^2 - 8^2 to you'll need to find 12 ratios...
If you're going from angle B, then they would look like so: sin(B) = opposite/hypotenuse = b/c cos(B) = adjacent/hypotenuse = a/c tan(B) = opposite/adjacent = b/a sec(B) = hypotenuse/adjacent = c/a csc(B) = hypotenuse/opposite = c/b cot(B) = adjacent/opposite = a/b The sec is a flipped cos, the csc is a flipped sin, and the cot is a flipped tan.
Still trying to figure what the value of a is. I know you do I turn it to: a^2+b^2=c^2 a^2+8^2=11^2 a^2+64=121 and A^2=54 so that makes it a = \[\sqrt{54}\] However how do I rationalize 54 again? would it be: \[\sqrt{9}*\sqrt{6}\] which would be: \[3\sqrt{6}\] or am I doing it wrong?
You're rationalizing it correctly....but 121-64 doesn't equal 54.
lol punched it in wrong on my calc. rofl. ok so 57 and I can't rationalize that down any further from what I can tell.
Happens allllll the time, haha. Yep, there's no way to really rationalize it further, so you can move on.

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