What is the general solution for (87.17)/(sin(120))=(40)/(sin(x)) ?

The general solution for (87.17)/(sin(120))=(40)/(sin(x)) is x=0.40867…+360n,x=180-0.40867…+360n

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(87.17)/(sin(120))=(40)/(sin(x))

\frac{87.17}{sin ( 12 0 ^{\circ} )} = \frac{40}{sin ( x )}

x = 0.40867 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40867 \dots + 36 0^{\circ} n

Solution steps

\frac{87.17}{sin ( 12 0 ^{\circ} )} = \frac{40}{sin ( x )}

sin (12 0^{\circ}) = \frac{3}{2}

\frac{87.17}{\frac{3}{2}} = \frac{40}{sin ( x )}

Cross multiply

87.17 sin (x) = 203

Multiply both sides by

100

8717 sin (x) = 20003

Divide both sides by

8717

sin (x) = \frac{2000 3}{8717}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{2000 3}{8717}

Apply trig inverse properties

x = arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.40867 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40867 \dots + 36 0^{\circ} n

23 tan (x) - 2 = 0

2 cos (x) 2 = 0

cos^{2} (x) - 6 cos (x) = - 9

cos (x) - 3 = 0

sec (x) - tan (x) = 3

What is the general solution for (87.17)/(sin(120))=(40)/(sin(x)) ?
The general solution for (87.17)/(sin(120))=(40)/(sin(x)) is x=0.40867…+360n,x=180-0.40867…+360n