Solve w/sin(18)=15/sin(137)

$$\frac{ w }{ \sin ( 18 ) } = \frac{ 15 }{ \sin ( 137 ) }$$

Solve for w

$$w = \frac{3090169943749474}{454665573374999} = 6\frac{362176503499480}{454665573374999} \approx 6.796577803$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{w}{0.3090169943749474} = \frac{15}{0.6819983600624985}$$

Expand \frac{15}{0.6819983600624985} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{w}{0.3090169943749474}=\frac{150000000000000000}{6819983600624985}$$

Reduce the fraction \frac{150000000000000000}{6819983600624985} to lowest terms by extracting and canceling out 15.

$$\frac{w}{0.3090169943749474}=\frac{10000000000000000}{454665573374999}$$

Multiply both sides by 0.3090169943749474.

$$w=\frac{10000000000000000}{454665573374999}\times 0.3090169943749474$$

Convert decimal number 0.3090169943749474 to fraction \frac{1545084971874737}{10000000000}. Reduce the fraction \frac{1545084971874737}{10000000000} to lowest terms by extracting and canceling out 1.

$$w=\frac{10000000000000000}{454665573374999}\times \frac{1545084971874737}{5000000000000000}$$

Multiply \frac{10000000000000000}{454665573374999} times \frac{1545084971874737}{5000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{10000000000000000\times 1545084971874737}{454665573374999\times 5000000000000000}$$

Do the multiplications in the fraction \frac{10000000000000000\times 1545084971874737}{454665573374999\times 5000000000000000}.

$$w=\frac{15450849718747370000000000000000}{2273327866874995000000000000000}$$

Reduce the fraction \frac{15450849718747370000000000000000}{2273327866874995000000000000000} to lowest terms by extracting and canceling out 5000000000000000.

$$w=\frac{3090169943749474}{454665573374999}$$