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# sinC/20 = sin65/19, how it gets to C=arcsin(20sin65/19)=73

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sinC/20 = sin65/19, how it gets to C=arcsin(20sin65/19)=73

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May 30, 2017

#1
+7352
+2

$$\frac{\sin C}{20}=\frac{\sin 65^{\circ}}{19}$$

Multiply both sides of the equation by 20.

$$\sin C=20\,*\,\frac{\sin 65^{\circ}}{19} \\~\\ \sin C = \frac{20\sin 65^{\circ}}{19}$$

Take the arcsin of both sides of the equation.

$$C = \arcsin(\frac{20\sin 65^{\circ}}{19})$$

So...putting this into a calculator gives us

$$C\approx72.556^{\circ}$$

.
May 30, 2017

#1
+7352
+2

$$\frac{\sin C}{20}=\frac{\sin 65^{\circ}}{19}$$

Multiply both sides of the equation by 20.

$$\sin C=20\,*\,\frac{\sin 65^{\circ}}{19} \\~\\ \sin C = \frac{20\sin 65^{\circ}}{19}$$

Take the arcsin of both sides of the equation.

$$C = \arcsin(\frac{20\sin 65^{\circ}}{19})$$

So...putting this into a calculator gives us

$$C\approx72.556^{\circ}$$

hectictar May 30, 2017