Solve 9/sin45=

$$\frac { 9 } { \sin 45 } =$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

Solution Steps

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

$$\frac{9}{\frac{\sqrt{2}}{2}}$$

Divide 9 by \frac{\sqrt{2}}{2} by multiplying 9 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{9\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{9\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{9\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{9\times 2\sqrt{2}}{2}$$

Multiply 9 and 2 to get 18.

$$\frac{18\sqrt{2}}{2}$$

Divide 18\sqrt{2} by 2 to get 9\sqrt{2}.

$$9\sqrt{2}$$