Solve 12sin45^circ/sin60^circ

$$\frac { 12 \sin 45 ^ { \circ } } { \sin 60 ^ { \circ } }$$

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

Solution Steps

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

$$\frac{12\times \frac{\sqrt{2}}{2}}{\sin(60)}$$

Cancel out 2, the greatest common factor in 12 and 2.

$$\frac{6\sqrt{2}}{\sin(60)}$$

Get the value of \sin(60) from trigonometric values table.

$$\frac{6\sqrt{2}}{\frac{\sqrt{3}}{2}}$$

Divide 6\sqrt{2} by \frac{\sqrt{3}}{2} by multiplying 6\sqrt{2} by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{6\sqrt{2}\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{6\sqrt{2}\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{2}\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{2}\times 2\sqrt{3}}{3}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{12\sqrt{6}}{3}$$

Divide 12\sqrt{6} by 3 to get 4\sqrt{6}.

$$4\sqrt{6}$$