Solve 3.7/sin25^circ=b/sin55^circ

$$\frac { 3.7 } { \sin 25 ^ { \circ } } = \frac { b } { \sin 55 ^ { \circ } }$$

Solve for b

$$b = \frac{151543128193463483}{21130913087034972} = 7\frac{3626736584218684}{21130913087034972} \approx 7.171631797$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{3.7}{0.42261826174069944} = \frac{b}{0.8191520442889918}$$

Expand \frac{3.7}{0.42261826174069944} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{370000000000000000}{42261826174069944}=\frac{b}{0.8191520442889918}$$

Reduce the fraction \frac{370000000000000000}{42261826174069944} to lowest terms by extracting and canceling out 8.

$$\frac{46250000000000000}{5282728271758743}=\frac{b}{0.8191520442889918}$$

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

$$\frac{b}{0.8191520442889918}=\frac{46250000000000000}{5282728271758743}$$

Multiply both sides by 0.8191520442889918.

$$b=\frac{46250000000000000}{5282728271758743}\times 0.8191520442889918$$

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.

$$b=\frac{46250000000000000}{5282728271758743}\times \frac{4095760221444959}{5000000000000000}$$

Multiply \frac{46250000000000000}{5282728271758743} times \frac{4095760221444959}{5000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$b=\frac{46250000000000000\times 4095760221444959}{5282728271758743\times 5000000000000000}$$

Do the multiplications in the fraction \frac{46250000000000000\times 4095760221444959}{5282728271758743\times 5000000000000000}.

$$b=\frac{189428910241829353750000000000000}{26413641358793715000000000000000}$$

Reduce the fraction \frac{189428910241829353750000000000000}{26413641358793715000000000000000} to lowest terms by extracting and canceling out 1250000000000000.

$$b=\frac{151543128193463483}{21130913087034972}$$