Solve 45^circ+sqrt{3}sin60^circ-(sqrt{3}/3

$$45 ^ { \circ } + \sqrt { 3 } \sin 60 ^ { \circ } - ( \sqrt { 3 } / 3$$

Evaluate

$$-\frac{\sqrt{3}}{3}+\frac{93}{2}\approx 45.922649731$$

Short Solution Steps

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

$$45+\sqrt{3}\times \frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{3}$$

Express \sqrt{3}\times \frac{\sqrt{3}}{2} as a single fraction.

$$45+\frac{\sqrt{3}\sqrt{3}}{2}-\frac{\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 45 times \frac{2}{2}.

$$\frac{45\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}-\frac{\sqrt{3}}{3}$$

Since \frac{45\times 2}{2} and \frac{\sqrt{3}\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

$$\frac{45\times 2+\sqrt{3}\sqrt{3}}{2}-\frac{\sqrt{3}}{3}$$

Do the multiplications in 45\times 2+\sqrt{3}\sqrt{3}.

$$\frac{90+3}{2}-\frac{\sqrt{3}}{3}$$

Do the calculations in 90+3.

$$\frac{93}{2}-\frac{\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{93}{2} times \frac{3}{3}. Multiply \frac{\sqrt{3}}{3} times \frac{2}{2}.

$$\frac{93\times 3}{6}-\frac{2\sqrt{3}}{6}$$

Since \frac{93\times 3}{6} and \frac{2\sqrt{3}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{93\times 3-2\sqrt{3}}{6}$$

Do the multiplications in 93\times 3-2\sqrt{3}.

$$\frac{279-2\sqrt{3}}{6}$$