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loser123456789

  • 3 years ago

I am really stuck someone help

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  1. loser123456789
    • 3 years ago
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    Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

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  2. valentinekid
    • 3 years ago
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    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
    • 3 years ago
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    sin?

  4. valentinekid
    • 3 years ago
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    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
    • 3 years ago
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    then we solve for x, right?...

  6. valentinekid
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    Multiply what by both sides? we have \[x*\cos(24)=11\] How do get x by itself?

  9. valentinekid
    • 3 years ago
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    What should we divide by?

  10. valentinekid
    • 3 years ago
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    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
    • 3 years ago
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    Not quite. \[\frac{1}{\cos(24)}*x*\cos(24)=11*\frac{1}{\cos(24)}\]

  12. valentinekid
    • 3 years ago
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    It's okay. What happens when we simplify that expression? Can we cancel anything out?

  13. valentinekid
    • 3 years ago
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    Yes! Exactly. The cos(24) cancels out on the left leaving us with x=11/cos(24).

  14. valentinekid
    • 3 years ago
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    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
    • 3 years ago
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    Yeah, just post another question and tag me in a comment.

  16. valentinekid
    • 3 years ago
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    New question. Where it says "ask a question..."

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