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# Trig Question

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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
+81
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$$\frac{sin(33.2)}{x}=\frac{sin(45.6)}{13.7}$$

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

Apr 24, 2019