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I am given that (sin 33.2 degrees)/(x) = (sin 45.6 degrees)/(13.7).

I am supposed to find all real numbers that satisfy the equation above and round approximate answers to 2 decimal places. How do I solve a problem like this?

 Apr 24, 2019
 #1
avatar+81 
+1

\(\frac{sin(33.2)}{x}=\frac{sin(45.6)}{13.7}\)

Alright, so the first thing you want to do here is to find the values of the sine functions.

\(sin(33.2) = 0.547563223493\)

Which rounded to 2 decimal places is 0.55.

\(sin(45.6) = 0.714472679633​\)

Rounded to 2 decimal places that's 0.72 (the 7 behind the two 4's carries down the line).

So, now we have: \(\frac{0.55}{x}=\frac{0.72}{13.7}\)

Then you have to cross multiply.

\(0.72x=(13.7)(0.55)\)

Then multiply 13.7 by 0.55.

\((13.7)(0.55) = 7.535​\)

Round to 7.54

\(0.72x=7.54\)

Then divide both sides by 0.72.

\(7.54/0.72 = 10.4722222222222222\)

Round that to 10.47

\(x=10.47\)

Does that make sense?

 Apr 24, 2019
 #2
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This is the answer that I got, but should there be more than one answer? Or is 10.47 sufficient

Guest Apr 24, 2019
 #3
avatar+81 
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10.47 should be sufficient since you aren't finding all possible values of the sine function and there isn't a squared anywhere.

MemeLord  Apr 24, 2019
 #4
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To two decimal places, the answer is 10.50.

You both need to check your arithmetic.

 Apr 24, 2019
 #5
avatar+18754 
+1

x = 13.7 * sin 33.2  / sin 45.6 = 10.49951  ~~ 10.50  (rounded)

 Apr 24, 2019

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