Question

I am really stuck someone help

Answer 1

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

Answer 2

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?)

Answer 3

sin?

Answer 4

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:
\[\cos(24)=\frac{11}{x}\]

Answer 5

then we solve for x, right?...

Answer 6

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

Answer 7

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?

Answer 8

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

Answer 9

What should we divide by?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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)

Answer 15

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

Answer 16

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