Solve C/sin55^circ=10/sin35^circ

$$\frac { C } { \sin 55 ^ { \circ } } = \frac { 10 } { \sin 35 ^ { \circ } }$$

Solve for C

$$C = \frac{4095760221444959}{286788218175523} = 14\frac{80725166987637}{286788218175523} \approx 14.281480067$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{C}{0.8191520442889918} = \frac{10}{0.573576436351046}$$

Expand \frac{10}{0.573576436351046} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{C}{0.8191520442889918}=\frac{10000000000000000}{573576436351046}$$

Reduce the fraction \frac{10000000000000000}{573576436351046} to lowest terms by extracting and canceling out 2.

$$\frac{C}{0.8191520442889918}=\frac{5000000000000000}{286788218175523}$$

Multiply both sides by 0.8191520442889918.

$$C=\frac{5000000000000000}{286788218175523}\times 0.8191520442889918$$

Convert decimal number 0.8191520442889918 to fraction \frac{4095760221444959}{10000000000}. Reduce the fraction \frac{4095760221444959}{10000000000} to lowest terms by extracting and canceling out 1.

$$C=\frac{5000000000000000}{286788218175523}\times \frac{4095760221444959}{5000000000000000}$$

Multiply \frac{5000000000000000}{286788218175523} times \frac{4095760221444959}{5000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$C=\frac{5000000000000000\times 4095760221444959}{286788218175523\times 5000000000000000}$$

Cancel out 5000000000000000 in both numerator and denominator.

$$C=\frac{4095760221444959}{286788218175523}$$