Solve 21sqrt{6}divsin(60)*sin(45)

$$21 \sqrt{ 6 } \div \sin ( 60 ) \times \sin ( 45 )$$

Evaluate

$$42$$

Solution Steps

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

$$\frac{21\sqrt{6}}{\frac{\sqrt{3}}{2}}\sin(45)$$

Divide 21\sqrt{6} by \frac{\sqrt{3}}{2} by multiplying 21\sqrt{6} by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{21\sqrt{6}\times 2}{\sqrt{3}}\sin(45)$$

Rationalize the denominator of \frac{21\sqrt{6}\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{21\sqrt{6}\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sin(45)$$

The square of \sqrt{3} is 3.

$$\frac{21\sqrt{6}\times 2\sqrt{3}}{3}\sin(45)$$

Multiply 21 and 2 to get 42.

$$\frac{42\sqrt{6}\sqrt{3}}{3}\sin(45)$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{42\sqrt{3}\sqrt{2}\sqrt{3}}{3}\sin(45)$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{42\times 3\sqrt{2}}{3}\sin(45)$$

Cancel out 3 and 3.

$$42\sqrt{2}\sin(45)$$

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

$$42\sqrt{2}\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 42 and 2.

$$21\sqrt{2}\sqrt{2}$$

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

$$21\times 2$$

Multiply 21 and 2 to get 42.

$$42$$