Solve 100divcos(45)

$$100 \div \cos ( 45 )$$

Evaluate

$$100\sqrt{2}\approx 141.421356237$$

Solution Steps

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

$$\frac{100}{\frac{\sqrt{2}}{2}}$$

Divide 100 by \frac{\sqrt{2}}{2} by multiplying 100 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{100\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{100\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{100\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{100\times 2\sqrt{2}}{2}$$

Multiply 100 and 2 to get 200.

$$\frac{200\sqrt{2}}{2}$$

Divide 200\sqrt{2} by 2 to get 100\sqrt{2}.

$$100\sqrt{2}$$