Solve 3tan30^circ+cos30^circ+2sin60^circ

$$3 \tan 30 ^ { \circ } + \cos 30 ^ { \circ } + 2 \sin 60 ^ { \circ }$$

Evaluate

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

Solution Steps

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

$$3\times \frac{\sqrt{3}}{3}+\cos(30)+2\sin(60)$$

Cancel out 3 and 3.

$$\sqrt{3}+\cos(30)+2\sin(60)$$

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

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

Combine \sqrt{3} and \frac{\sqrt{3}}{2} to get \frac{3}{2}\sqrt{3}.

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

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

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

Cancel out 2 and 2.

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

Combine \frac{3}{2}\sqrt{3} and \sqrt{3} to get \frac{5}{2}\sqrt{3}.

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