What is the general solution for (26.4575)/(sin(60))=(20)/(sin(B)) ?

The general solution for (26.4575)/(sin(60))=(20)/(sin(B)) is B=0.71372…+360n,B=180-0.71372…+360n

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(26.4575)/(sin(60))=(20)/(sin(B))

\frac{26.4575}{sin ( 6 0 ^{\circ} )} = \frac{20}{sin ( B )}

B = 0.71372 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.71372 \dots + 36 0^{\circ} n

Solution steps

\frac{26.4575}{sin ( 6 0 ^{\circ} )} = \frac{20}{sin ( B )}

sin (6 0^{\circ}) = \frac{3}{2}

\frac{26.4575}{\frac{3}{2}} = \frac{20}{sin ( B )}

Cross multiply

26.4575 sin (B) = 103

Divide both sides by

26.4575

sin (B) = \frac{10 3}{26.4575}

Verify Solutions

Find undefined (singularity) points:

sin (B) = 0

Combine undefined points with solutions:

sin (B) = \frac{10 3}{26.4575}

Apply trig inverse properties

B = arcsin (\frac{10 3}{26.4575}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{10 3}{26.4575}) + 36 0^{\circ} n

Show solutions in decimal form

B = 0.71372 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.71372 \dots + 36 0^{\circ} n

sin (\frac{5}{2} θ) = - 0.966

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

0 = - 8 sin (x)

cos^{2} (x) + 2 cos (x) + 1 = 0, (0, 2 π)

3 sin (2 θ) = 2 sin (θ)

What is the general solution for (26.4575)/(sin(60))=(20)/(sin(B)) ?
The general solution for (26.4575)/(sin(60))=(20)/(sin(B)) is B=0.71372…+360n,B=180-0.71372…+360n