Solve \frac{\sin 45^\circ}{5}=\frac{\sin 60^\circ}{x}

Evaluate

\frac{sin ( 4 5 ^{\circ} )}{5} = \frac{sin ( 6 0 ^{\circ} )}{x}

Find the domain

\frac{sin ( 4 5 ^{\circ} )}{5} = \frac{sin ( 6 0 ^{\circ} )}{x}, x \neq = 0

Rewrite the expression

\frac{2}{10} = \frac{sin ( 6 0 ^{\circ} )}{x}

Rewrite the expression

\frac{2}{10} = \frac{3}{2 x}

Swap the sides of the equation

\frac{3}{2 x} = \frac{2}{10}

Rewrite the expression

2 x = \frac{3 \times 10}{2}

Divide the terms

2 x = \frac{10 3}{2}

Multiply by the reciprocal

2 x \times \frac{1}{2} = \frac{10 3}{2} \times \frac{1}{2}

Multiply

x = \frac{10 3}{2} \times \frac{1}{2}

Multiply

More Steps

x = \frac{5 3}{2}

Rearrange the numbers

More Steps

x = \frac{5 6}{2}

Check if the solution is in the defined range

x = \frac{5 6}{2}, x \neq = 0

Solution

x = \frac{5 6}{2}

Alternative Form

x \approx 6.123724

\frac{\sin 45^\circ}{5}=\frac{\sin 60^\circ}{x}