What is the general solution for (125)/(sin(110))=(100)/(sin(b)) ?

The general solution for (125)/(sin(110))=(100)/(sin(b)) is b=0.85071…+360n,b=180-0.85071…+360n

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(125)/(sin(110))=(100)/(sin(b))

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

b = 0.85071 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.85071 \dots + 36 0^{\circ} n

Solution steps

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

Cross multiply

125 sin (b) = sin (11 0^{\circ}) \cdot 100

Divide both sides by

125

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

Verify Solutions

Find undefined (singularity) points:

sin (b) = 0

Combine undefined points with solutions:

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

Apply trig inverse properties

b = arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.85071 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.85071 \dots + 36 0^{\circ} n

tan (\frac{2 x}{3}) - 3 = 0

2 sin^{2} (x) - cos^{2} (x) - 2 = 0

cos (3 x) \cdot 3 = 0

16 sec^{2} (θ) - 25 = 0

2 csc^{2} (x) - 4 = 0

What is the general solution for (125)/(sin(110))=(100)/(sin(b)) ?
The general solution for (125)/(sin(110))=(100)/(sin(b)) is b=0.85071…+360n,b=180-0.85071…+360n