Solve sin35^circ/a=sin88^circ/44

$$\frac { \sin 35 ^ { \circ } } { a } = \frac { \sin 88 ^ { \circ } } { 44 }$$

Solve for a

$$a = \frac{126186815997230120}{4996954135095479} = 25\frac{1262962619843137}{4996954135095479} \approx 25.25274649$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.573576436351046}{a} = \frac{0.9993908270190958}{44}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 44a, the least common multiple of a,44.

$$44\times 0.573576436351046=a\times 0.9993908270190958$$

Multiply 44 and 0.573576436351046 to get 25.237363199446024.

$$25.237363199446024=a\times 0.9993908270190958$$

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

$$a\times 0.9993908270190958=25.237363199446024$$

Divide both sides by 0.9993908270190958.

$$a=\frac{25.237363199446024}{0.9993908270190958}$$

Expand \frac{25.237363199446024}{0.9993908270190958} by multiplying both numerator and the denominator by 10000000000000000.

$$a=\frac{252373631994460240}{9993908270190958}$$

Reduce the fraction \frac{252373631994460240}{9993908270190958} to lowest terms by extracting and canceling out 2.

$$a=\frac{126186815997230120}{4996954135095479}$$