Solve 127.3div0.5div18divsin(45)

$$127.3 \div 0.5 \div 18 \div \sin ( 45 )$$

Evaluate

$$\frac{1273\sqrt{2}}{90}\approx 20.003265166$$

Solution Steps

Express \frac{\frac{127.3}{0.5}}{18} as a single fraction.

$$\frac{\frac{127.3}{0.5\times 18}}{\sin(45)}$$

Multiply 0.5 and 18 to get 9.

$$\frac{\frac{127.3}{9}}{\sin(45)}$$

Expand \frac{127.3}{9} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{1273}{90}}{\sin(45)}$$

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

$$\frac{\frac{1273}{90}}{\frac{\sqrt{2}}{2}}$$

Divide \frac{1273}{90} by \frac{\sqrt{2}}{2} by multiplying \frac{1273}{90} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{1273\times 2}{90\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1273}{45\sqrt{2}}$$

Rationalize the denominator of \frac{1273}{45\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1273\sqrt{2}}{45\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1273\sqrt{2}}{45\times 2}$$

Multiply 45 and 2 to get 90.

$$\frac{1273\sqrt{2}}{90}$$