Solve sin132^circ/a=26.5/5.1

$$\frac { \sin 132 ^ { \circ } } { a } = \frac { 26.5 } { 5.1 }$$

Solve for a

$$a=\frac{189501930496735521}{1325000000000000000}\approx 0.143020325$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.7431448254773942}{a} = \frac{26.5}{5.1}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$0.7431448254773942=a\times \frac{26.5}{5.1}$$

Expand \frac{26.5}{5.1} by multiplying both numerator and the denominator by 10.

$$0.7431448254773942=a\times \frac{265}{51}$$

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

$$a\times \frac{265}{51}=0.7431448254773942$$

Multiply both sides by \frac{51}{265}, the reciprocal of \frac{265}{51}.

$$a=0.7431448254773942\times \frac{51}{265}$$

Convert decimal number 0.7431448254773942 to fraction \frac{3715724127386971}{10000000000}. Reduce the fraction \frac{3715724127386971}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{3715724127386971}{5000000000000000}\times \frac{51}{265}$$

Multiply \frac{3715724127386971}{5000000000000000} times \frac{51}{265} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{3715724127386971\times 51}{5000000000000000\times 265}$$

Do the multiplications in the fraction \frac{3715724127386971\times 51}{5000000000000000\times 265}.

$$a=\frac{189501930496735521}{1325000000000000000}$$