Solve 16(cos45^circ)+7(tan30^circ)

$$16 ( \cos 45 ^ { \circ } ) + 7 ( \tan 30 ^ { \circ } )$$

Evaluate

$$\frac{7\sqrt{3}}{3}+8\sqrt{2}\approx 15.355160383$$

Short Solution Steps

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

$$16\times \frac{\sqrt{2}}{2}+7\tan(30)$$

Cancel out 2, the greatest common factor in 16 and 2.

$$8\sqrt{2}+7\tan(30)$$

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

$$8\sqrt{2}+7\times \frac{\sqrt{3}}{3}$$

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

$$8\sqrt{2}+\frac{7\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8\sqrt{2} times \frac{3}{3}.

$$\frac{3\times 8\sqrt{2}}{3}+\frac{7\sqrt{3}}{3}$$

Since \frac{3\times 8\sqrt{2}}{3} and \frac{7\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\times 8\sqrt{2}+7\sqrt{3}}{3}$$

Do the multiplications in 3\times 8\sqrt{2}+7\sqrt{3}.

$$\frac{24\sqrt{2}+7\sqrt{3}}{3}$$