Solve (1+cos30^circ)*20/sin30^circ

$$\frac { ( 1 + \cos 30 ^ { \circ } ) \times 20 } { \sin 30 ^ { \circ } }$$

Evaluate

$$20\left(\sqrt{3}+2\right)\approx 74.641016151$$

Solution Steps

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

$$\frac{20\left(1+\frac{\sqrt{3}}{2}\right)}{\sin(30)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{20\left(\frac{2}{2}+\frac{\sqrt{3}}{2}\right)}{\sin(30)}$$

Since \frac{2}{2} and \frac{\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

$$\frac{20\times \frac{2+\sqrt{3}}{2}}{\sin(30)}$$

Cancel out 2, the greatest common factor in 20 and 2.

$$\frac{10\left(2+\sqrt{3}\right)}{\sin(30)}$$

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

$$\frac{10\left(2+\sqrt{3}\right)}{\frac{1}{2}}$$

Divide 10\left(2+\sqrt{3}\right) by \frac{1}{2} to get 20\left(2+\sqrt{3}\right).

$$20\left(2+\sqrt{3}\right)$$

Use the distributive property to multiply 20 by 2+\sqrt{3}.

$$40+20\sqrt{3}$$