Solve frac{3sqrt{2}}{sin(45)}*sin(20)

$$\frac{ 3 \sqrt{ 2 } }{ \sin ( 45 ) } \times \sin ( 20 )$$

Evaluate

$$2.0521208599540122$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3 \sqrt{2}}{\sin(45)} \cdot 0.3420201433256687$$

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

$$0.3420201433256687\times \frac{3\sqrt{2}}{\frac{\sqrt{2}}{2}}$$

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

$$0.3420201433256687\times \frac{3\sqrt{2}\times 2}{\sqrt{2}}$$

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

$$0.3420201433256687\times \frac{3\sqrt{2}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$0.3420201433256687\times \frac{3\sqrt{2}\times 2\sqrt{2}}{2}$$

Multiply 3 and 2 to get 6.

$$0.3420201433256687\times \frac{6\sqrt{2}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$0.3420201433256687\times \frac{6\times 2}{2}$$

Multiply 6 and 2 to get 12.

$$0.3420201433256687\times \frac{12}{2}$$

Divide 12 by 2 to get 6.

$$0.3420201433256687\times 6$$

Multiply 0.3420201433256687 and 6 to get 2.0521208599540122.

$$2.0521208599540122$$