Solve b/sin48^circ=86/sin75^circ

$$\frac { b } { \sin 48 ^ { \circ } } = \frac { 86 } { \sin 75 ^ { \circ } }$$

Solve for b

$$b = \frac{14862896509547882}{224633913090481} = 66\frac{37058245576136}{224633913090481} \approx 66.164971731$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{b}{0.7431448254773941} = \frac{86}{0.9659258262890683}$$

Expand \frac{86}{0.9659258262890683} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{b}{0.7431448254773941}=\frac{860000000000000000}{9659258262890683}$$

Reduce the fraction \frac{860000000000000000}{9659258262890683} to lowest terms by extracting and canceling out 43.

$$\frac{b}{0.7431448254773941}=\frac{20000000000000000}{224633913090481}$$

Multiply both sides by 0.7431448254773941.

$$b=\frac{20000000000000000}{224633913090481}\times 0.7431448254773941$$

Convert decimal number 0.7431448254773941 to fraction \frac{7431448254773941}{10000000000}. Reduce the fraction \frac{7431448254773941}{10000000000} to lowest terms by extracting and canceling out 1.

$$b=\frac{20000000000000000}{224633913090481}\times \frac{7431448254773941}{10000000000000000}$$

Multiply \frac{20000000000000000}{224633913090481} times \frac{7431448254773941}{10000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$b=\frac{20000000000000000\times 7431448254773941}{224633913090481\times 10000000000000000}$$

Do the multiplications in the fraction \frac{20000000000000000\times 7431448254773941}{224633913090481\times 10000000000000000}.

$$b=\frac{148628965095478820000000000000000}{2246339130904810000000000000000}$$

Reduce the fraction \frac{148628965095478820000000000000000}{2246339130904810000000000000000} to lowest terms by extracting and canceling out 10000000000000000.

$$b=\frac{14862896509547882}{224633913090481}$$