Solve 12/cos30

$$\frac { 12 } { \cos 30 }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

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

$$\frac{12}{\frac{\sqrt{3}}{2}}$$

Divide 12 by \frac{\sqrt{3}}{2} by multiplying 12 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{12\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{12\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{12\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{12\times 2\sqrt{3}}{3}$$

Multiply 12 and 2 to get 24.

$$\frac{24\sqrt{3}}{3}$$

Divide 24\sqrt{3} by 3 to get 8\sqrt{3}.

$$8\sqrt{3}$$