Solve 15cos(45)+7tan(30)

$$15 \cos ( 45 ) +7 \tan ( 30 )$$

Evaluate

$$\frac{7\sqrt{3}}{3}+\frac{15\sqrt{2}}{2}\approx 14.648053602$$

Short Solution Steps

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

$$15\times \frac{\sqrt{2}}{2}+7\tan(30)$$

Express 15\times \frac{\sqrt{2}}{2} as a single fraction.

$$\frac{15\sqrt{2}}{2}+7\tan(30)$$

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

$$\frac{15\sqrt{2}}{2}+7\times \frac{\sqrt{3}}{3}$$

Express 7\times \frac{\sqrt{3}}{3} as a single fraction.

$$\frac{15\sqrt{2}}{2}+\frac{7\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{15\sqrt{2}}{2} times \frac{3}{3}. Multiply \frac{7\sqrt{3}}{3} times \frac{2}{2}.

$$\frac{3\times 15\sqrt{2}}{6}+\frac{2\times 7\sqrt{3}}{6}$$

Since \frac{3\times 15\sqrt{2}}{6} and \frac{2\times 7\sqrt{3}}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\times 15\sqrt{2}+2\times 7\sqrt{3}}{6}$$

Do the multiplications in 3\times 15\sqrt{2}+2\times 7\sqrt{3}.

$$\frac{45\sqrt{2}+14\sqrt{3}}{6}$$