anonymous 4 years ago 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

1. xkehaulanix

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.

2. anonymous

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.

3. xkehaulanix

Okay, so the Pythagorean theorem states that $a^2+b^2=c^2$ If you rearrange it to find a, it would become $a=\sqrt[2]{c^2-b^2}$

4. xkehaulanix

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.

5. campbell_st

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...

6. xkehaulanix

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.

7. anonymous

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?

8. xkehaulanix

You're rationalizing it correctly....but 121-64 doesn't equal 54.

9. anonymous

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.

10. xkehaulanix

Happens allllll the time, haha. Yep, there's no way to really rationalize it further, so you can move on.