Solve a/sin106=22/sin15

$$\frac { a } { \sin 106 } = \frac { 22 } { \sin 15 }$$

Solve for a

$$a = \frac{1057387865532150790}{12940952255126037} = 81\frac{9170732866941868}{12940952255126036} \approx 81.708659818$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{a}{0.9612616959383189} = \frac{22}{0.25881904510252074}$$

Expand \frac{22}{0.25881904510252074} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{a}{0.9612616959383189}=\frac{2200000000000000000}{25881904510252074}$$

Reduce the fraction \frac{2200000000000000000}{25881904510252074} to lowest terms by extracting and canceling out 2.

$$\frac{a}{0.9612616959383189}=\frac{1100000000000000000}{12940952255126037}$$

Multiply both sides by 0.9612616959383189.

$$a=\frac{1100000000000000000}{12940952255126037}\times 0.9612616959383189$$

Convert decimal number 0.9612616959383189 to fraction \frac{9612616959383189}{10000000000}. Reduce the fraction \frac{9612616959383189}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{1100000000000000000}{12940952255126037}\times \frac{9612616959383189}{10000000000000000}$$

Multiply \frac{1100000000000000000}{12940952255126037} times \frac{9612616959383189}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{1100000000000000000\times 9612616959383189}{12940952255126037\times 10000000000000000}$$

Do the multiplications in the fraction \frac{1100000000000000000\times 9612616959383189}{12940952255126037\times 10000000000000000}.

$$a=\frac{10573878655321507900000000000000000}{129409522551260370000000000000000}$$

Reduce the fraction \frac{10573878655321507900000000000000000}{129409522551260370000000000000000} to lowest terms by extracting and canceling out 10000000000000000.

$$a=\frac{1057387865532150790}{12940952255126037}$$