Solve 10/sin(60)*10

$$\frac{ 10 }{ \sin ( 60 ) } \times 10$$

Evaluate

$$\frac{200\sqrt{3}}{3}\approx 115.470053838$$

Solution Steps

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

$$10\times \frac{10}{\frac{\sqrt{3}}{2}}$$

Divide 10 by \frac{\sqrt{3}}{2} by multiplying 10 by the reciprocal of \frac{\sqrt{3}}{2}.

$$10\times \frac{10\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{10\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$10\times \frac{10\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$10\times \frac{10\times 2\sqrt{3}}{3}$$

Multiply 10 and 2 to get 20.

$$10\times \frac{20\sqrt{3}}{3}$$

Express 10\times \frac{20\sqrt{3}}{3} as a single fraction.

$$\frac{10\times 20\sqrt{3}}{3}$$

Multiply 10 and 20 to get 200.

$$\frac{200\sqrt{3}}{3}$$