Solve sin(30^circ)+2sin(60^circ)+sqrt{3}tan(45^circ)

$$\sin ( 30 ^ { \circ } ) +2 \sin ( 60 ^ { \circ } ) + \sqrt{ 3 } \tan ( 45 ^ { \circ } )$$

Evaluate

$$2\sqrt{3}+\frac{1}{2}\approx 3.964101615$$

Solution Steps

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

$$\frac{1}{2}+2\sin(60)+\sqrt{3}\tan(45)$$

Get the value of \sin(60) from trigonometric values table.

$$\frac{1}{2}+2\times \frac{\sqrt{3}}{2}+\sqrt{3}\tan(45)$$

Cancel out 2 and 2.

$$\frac{1}{2}+\sqrt{3}+\sqrt{3}\tan(45)$$

Get the value of \tan(45) from trigonometric values table.

$$\frac{1}{2}+\sqrt{3}+\sqrt{3}\times 1$$

Combine \sqrt{3} and \sqrt{3}\times 1 to get 2\sqrt{3}.

$$\frac{1}{2}+2\sqrt{3}$$