Solve sin127^circ/a=sin26.5^circ/5.1

$$\frac { \sin 127 ^ { \circ } } { a } = \frac { \sin 26.5 ^ { \circ } } { 5.1 }$$

Solve for a

$$a = \frac{407304110124119277}{44619781310980877} = 9\frac{5726078325291376}{44619781310980880} \approx 9.128330488$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.7986355100472927}{a} = \frac{0.44619781310980877}{5.1}$$

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

$$0.7986355100472927=a\times \frac{0.44619781310980877}{5.1}$$

Expand \frac{0.44619781310980877}{5.1} by multiplying both numerator and the denominator by 100000000000000000.

$$0.7986355100472927=a\times \frac{44619781310980877}{510000000000000000}$$

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

$$a\times \frac{44619781310980877}{510000000000000000}=0.7986355100472927$$

Multiply both sides by \frac{510000000000000000}{44619781310980877}, the reciprocal of \frac{44619781310980877}{510000000000000000}.

$$a=0.7986355100472927\times \frac{510000000000000000}{44619781310980877}$$

Convert decimal number 0.7986355100472927 to fraction \frac{7986355100472927}{10000000000}. Reduce the fraction \frac{7986355100472927}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{7986355100472927}{10000000000000000}\times \frac{510000000000000000}{44619781310980877}$$

Multiply \frac{7986355100472927}{10000000000000000} times \frac{510000000000000000}{44619781310980877} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{7986355100472927\times 510000000000000000}{10000000000000000\times 44619781310980877}$$

Do the multiplications in the fraction \frac{7986355100472927\times 510000000000000000}{10000000000000000\times 44619781310980877}.

$$a=\frac{4073041101241192770000000000000000}{446197813109808770000000000000000}$$

Reduce the fraction \frac{4073041101241192770000000000000000}{446197813109808770000000000000000} to lowest terms by extracting and canceling out 10000000000000000.

$$a=\frac{407304110124119277}{44619781310980877}$$