Solve 5divcos(30^circ)

$$5 \div \cos ( 30 ^ { \circ } )$$

Evaluate

$$\frac{10\sqrt{3}}{3}\approx 5.773502692$$

Solution Steps

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

$$\frac{5}{\frac{\sqrt{3}}{2}}$$

Divide 5 by \frac{\sqrt{3}}{2} by multiplying 5 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{5\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{5\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{5\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5\times 2\sqrt{3}}{3}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{3}}{3}$$