Solve 3.7/sin25^circ=c/sin100^circ

$$\frac { 3.7 } { \sin 25 ^ { \circ } } = \frac { c } { \sin 100 ^ { \circ } }$$

Solve for c

$$c = \frac{45547358576814620}{5282728271758743} = 8\frac{3285532402744680}{5282728271758743} \approx 8.621938558$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{3.7}{0.42261826174069944} = \frac{c}{0.984807753012208}$$

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

$$\frac{370000000000000000}{42261826174069944}=\frac{c}{0.984807753012208}$$

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

$$\frac{46250000000000000}{5282728271758743}=\frac{c}{0.984807753012208}$$

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

$$\frac{c}{0.984807753012208}=\frac{46250000000000000}{5282728271758743}$$

Multiply both sides by 0.984807753012208.

$$c=\frac{46250000000000000}{5282728271758743}\times 0.984807753012208$$

Convert decimal number 0.984807753012208 to fraction \frac{61550484563263}{10000000000}. Reduce the fraction \frac{61550484563263}{10000000000} to lowest terms by extracting and canceling out 1.

$$c=\frac{46250000000000000}{5282728271758743}\times \frac{61550484563263}{62500000000000}$$

Multiply \frac{46250000000000000}{5282728271758743} times \frac{61550484563263}{62500000000000} by multiplying numerator times numerator and denominator times denominator.

$$c=\frac{46250000000000000\times 61550484563263}{5282728271758743\times 62500000000000}$$

Do the multiplications in the fraction \frac{46250000000000000\times 61550484563263}{5282728271758743\times 62500000000000}.

$$c=\frac{2846709911050913750000000000000}{330170516984921437500000000000}$$

Reduce the fraction \frac{2846709911050913750000000000000}{330170516984921437500000000000} to lowest terms by extracting and canceling out 62500000000000.

$$c=\frac{45547358576814620}{5282728271758743}$$