Solve 7*sin(30)/sin(45)

$$\frac{ 7 \times \sin ( 30 ) }{ \sin ( 45 ) }$$

Evaluate

$$\frac{7\sqrt{2}}{2}\approx 4.949747468$$

Solution Steps

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

$$\frac{7\times \frac{1}{2}}{\sin(45)}$$

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{\frac{7}{2}}{\sin(45)}$$

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

$$\frac{\frac{7}{2}}{\frac{\sqrt{2}}{2}}$$

Divide \frac{7}{2} by \frac{\sqrt{2}}{2} by multiplying \frac{7}{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{7\times 2}{2\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7}{\sqrt{2}}$$

Rationalize the denominator of \frac{7}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7\sqrt{2}}{2}$$