Solve sin(60)*cos(30)/sin(45)*sin(60)

$$\frac{ \sin ( 60 ) \times \cos ( 30 ) }{ \sin ( 45 ) \times \sin ( 60 ) }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Cancel out \sin(60) in both numerator and denominator.

$$\frac{\cos(30)}{\sin(45)}$$

Get the value of \cos(30) from trigonometric values table.

$$\frac{\frac{\sqrt{3}}{2}}{\sin(45)}$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}}$$

Divide \frac{\sqrt{3}}{2} by \frac{\sqrt{2}}{2} by multiplying \frac{\sqrt{3}}{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{\sqrt{3}\times 2}{2\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}$$