Solve 2.5/tan30^circ

$$\frac { 2.5 } { \tan 30 ^ { \circ } }$$

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

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

$$\frac{2.5}{\frac{\sqrt{3}}{3}}$$

Divide 2.5 by \frac{\sqrt{3}}{3} by multiplying 2.5 by the reciprocal of \frac{\sqrt{3}}{3}.

$$\frac{2.5\times 3}{\sqrt{3}}$$

Rationalize the denominator of \frac{2.5\times 3}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2.5\times 3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2.5\times 3\sqrt{3}}{3}$$

Multiply 2.5 and 3 to get 7.5.

$$\frac{7.5\sqrt{3}}{3}$$

Divide 7.5\sqrt{3} by 3 to get 2.5\sqrt{3}.

$$2.5\sqrt{3}$$