Solve tan(30)*(120+40sqrt{3})

$$\tan ( 30 ) \times (120+40 \sqrt{ 3 } )$$

Evaluate

$$40\left(\sqrt{3}+1\right)\approx 109.282032303$$

Solution Steps

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

$$\frac{\sqrt{3}}{3}\left(120+40\sqrt{3}\right)$$

Express \frac{\sqrt{3}}{3}\left(120+40\sqrt{3}\right) as a single fraction.

$$\frac{\sqrt{3}\left(120+40\sqrt{3}\right)}{3}$$

Use the distributive property to multiply \sqrt{3} by 120+40\sqrt{3}.

$$\frac{120\sqrt{3}+40\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{120\sqrt{3}+40\times 3}{3}$$

Multiply 40 and 3 to get 120.

$$\frac{120\sqrt{3}+120}{3}$$