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If (1.33)sin(25) = (1.5)sin(theta), what is theta?

 

So far, I got this:

 

(1.33)sin(25) = (1.5)sin(theta)

 

sin(theta) = (1.33)sin(25) / (-0.11735188)

 

I don't know what else to do... a little help? Please?

 Jul 23, 2017
 #1
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I do not understand how you got to \(sin(\Theta)=1.33sin(\Theta)/(-0.1135188)\); however, this is how I would sove this equation.

 

\(1.33\times sin(25) = 1.5\times sin(\Theta)\)

 

\(1.33\times -0.132351750098 ≈ 1.5\times sin(\Theta)\)

 

\(-0.17602782763034 ≈ 1.5\times sin(\Theta)\)

 

\(\frac{-0.17602782763034}{1.5} ≈ \frac{1.5\times sin(\Theta)}{1.5}\)

 

\(\frac{-0.17602782763034}{1.5} ≈ \frac{1\times sin(\Theta)}{1}\)

 

\(\frac{-0.17602782763034}{1.5} ≈ 1\times sin(\Theta)\)

 

\(\frac{-0.17602782763034}{1.5} ≈ sin(\Theta)\)

 

\(-0.1173518850868933 ≈ sin(\Theta)\)

 

\({sin}^{-1}(-0.1173518850868933) ≈ {sin}^{-1}[sin(\Theta)]\)

 

\(-0.11762291934 ≈\Theta\)

 

\(\Theta≈-0.11762291934\)

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 Jul 23, 2017
edited by gibsonj338  Jul 23, 2017
 #2
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If (1.33)sin(25) = (1.5)sin(theta), what is theta?

 

1.33 x 0.42261826..... = 1.5sin(theta)

0.5620823.... = 1.5sin(theta)   divide both sides by 1.5

Sin(theta) =0.5620823 / 1.5

Sin(theta) = 0.37472152541.....

Theta = Sin^-1(0.37472152541)

Theta = 22 Degrees.

 Jul 23, 2017
 #3
avatar+99388 
-1

(1.33)sin(25) = (1.5)sin(theta)

 

I think if is reasonable to assume that the given angles is 25 degrees

 

\((1.33)sin(25) = (1.5)sin(\theta)\\ \frac{(1.33)sin(25) }{1.5}= \frac{(1.5)sin(\theta)}{1.5}\\ sin\theta = \frac{(1.33)sin(25) }{1.5}\)

 

1.33*sin(25)/1.5 = 0.3747215254103533

 

\(sin\theta = 0.3747215254103533\\ \theta =sin^{-1}0.3747215254103533\)

 

 

asin(0.3747215254103533) = 22.007102456653

 

\(\theta\approx 22^\circ\)

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 Jul 23, 2017

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