## anonymous 3 years ago I am really stuck someone help

1. anonymous

Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

2. anonymous

Trigonometric functions are Sin, Cos, and Tan defined as: Sin=opposite/hypotenuse Cos=adjacent/hypotenuse Tan=opposite/adjacent Which of these three is best suited for the diagram? (which pieces do you know?)

3. anonymous

sin?

4. anonymous

Cos, because we know the length of the leg adjacent to our angle(11) and we want to find the hypotenuse. So to solve this we setup the problem as follows: $\cos(24)=\frac{11}{x}$

5. anonymous

then we solve for x, right?...

6. anonymous

Yeah, we move x over to the other side by multiplying both sides by x. What happens when you evaluate: $x(\cos(24))=(\frac{11}{x})*x$

7. anonymous

Yes, but be careful when multiplying trig functions. cos(24x) is very different from cos(24)*x or x*cos(24). So we have x*cos(24)=11. How do we get x by itself?

8. anonymous

Multiply what by both sides? we have $x*\cos(24)=11$ How do get x by itself?

9. anonymous

What should we divide by?

10. anonymous

24 is a part of the cos function, so they're tied together. Divide by cos(24) and what do you end up with?

11. anonymous

Not quite. $\frac{1}{\cos(24)}*x*\cos(24)=11*\frac{1}{\cos(24)}$

12. anonymous

It's okay. What happens when we simplify that expression? Can we cancel anything out?

13. anonymous

Yes! Exactly. The cos(24) cancels out on the left leaving us with x=11/cos(24).

14. anonymous

Mmhmm. If you're allowed a calculator or you're asked to give an actual number, just evaluate in your calculator and you get 12.04, rounded. If you're just asked to find x, I would say leave it exact in the form of 11/cos(24)

15. anonymous

Yeah, just post another question and tag me in a comment.

16. anonymous

New question. Where it says "ask a question..."