Solve 17.5/sin48^circ=a/sin22^circ

$$\frac { 17.5 } { \sin 48 ^ { \circ } } = \frac { a } { \sin 22 ^ { \circ } }$$

Solve for a

$$a = \frac{65556153847784600}{7431448254773941} = 8\frac{6104567809593072}{7431448254773941} \approx 8.821450624$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{17.5}{0.7431448254773941} = \frac{a}{0.374606593415912}$$

Expand \frac{17.5}{0.7431448254773941} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{175000000000000000}{7431448254773941}=\frac{a}{0.374606593415912}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{a}{0.374606593415912}=\frac{175000000000000000}{7431448254773941}$$

Multiply both sides by 0.374606593415912.

$$a=\frac{175000000000000000}{7431448254773941}\times 0.374606593415912$$

Convert decimal number 0.374606593415912 to fraction \frac{46825824176989}{10000000000}. Reduce the fraction \frac{46825824176989}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{175000000000000000}{7431448254773941}\times \frac{46825824176989}{125000000000000}$$

Multiply \frac{175000000000000000}{7431448254773941} times \frac{46825824176989}{125000000000000} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{175000000000000000\times 46825824176989}{7431448254773941\times 125000000000000}$$

Do the multiplications in the fraction \frac{175000000000000000\times 46825824176989}{7431448254773941\times 125000000000000}.

$$a=\frac{8194519230973075000000000000000}{928931031846742625000000000000}$$

Reduce the fraction \frac{8194519230973075000000000000000}{928931031846742625000000000000} to lowest terms by extracting and canceling out 125000000000000.

$$a=\frac{65556153847784600}{7431448254773941}$$