## loser123456789 2 years ago I am really stuck someone help

1. loser123456789

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

2. valentinekid

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. loser123456789

sin?

4. valentinekid

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. valentinekid

then we solve for x, right?...

6. valentinekid

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. valentinekid

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. valentinekid

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

9. valentinekid

What should we divide by?

10. valentinekid

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. valentinekid

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

12. valentinekid

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

13. valentinekid

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

14. valentinekid

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. valentinekid

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

16. valentinekid

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