What is the general solution for (50)/(sin(105))=(20)/(sin(x)) ?

The general solution for (50)/(sin(105))=(20)/(sin(x)) is x=0.39669…+360n,x=180-0.39669…+360n

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(50)/(sin(105))=(20)/(sin(x))

\frac{50}{sin ( 10 5 ^{\circ} )} = \frac{20}{sin ( x )}

x = 0.39669 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.39669 \dots + 36 0^{\circ} n

Solution steps

\frac{50}{sin ( 10 5 ^{\circ} )} = \frac{20}{sin ( x )}

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

\frac{50}{\frac{2 ( 3 + 1 )}{4}} = \frac{20}{sin ( x )}

Cross multiply

50 sin (x) = 52 (1 + 3)

Divide both sides by

50

sin (x) = \frac{2 ( 1 + 3 )}{10}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{2 ( 1 + 3 )}{10}

Apply trig inverse properties

x = arcsin (\frac{2 ( 1 + 3 )}{10}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2 ( 1 + 3 )}{10}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.39669 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.39669 \dots + 36 0^{\circ} n

x, sin^{2} (x) = \frac{5 m - 5}{2}

csc (θ) = - 1.343

csc (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}, sin (θ)

\frac{2 - 3 sin ( θ )}{2} = - 3 sin (θ)

sin (2 x) = \frac{- 3}{2}

What is the general solution for (50)/(sin(105))=(20)/(sin(x)) ?
The general solution for (50)/(sin(105))=(20)/(sin(x)) is x=0.39669…+360n,x=180-0.39669…+360n