Solve sqrt{3}sin83^circ/sin60^circ

$$\sqrt { 3 } \frac { \sin 83 ^ { \circ } } { \sin 60 ^ { \circ } }$$

Evaluate

$$1.985092303282644$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{3} \frac{0.992546151641322}{\sin(60)}$$

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

$$\sqrt{3}\times \frac{0.992546151641322}{\frac{\sqrt{3}}{2}}$$

Divide 0.992546151641322 by \frac{\sqrt{3}}{2} by multiplying 0.992546151641322 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\sqrt{3}\times \frac{0.992546151641322\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{0.992546151641322\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}\times \frac{0.992546151641322\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{3}\times \frac{0.992546151641322\times 2\sqrt{3}}{3}$$

Multiply 0.992546151641322 and 2 to get 1.985092303282644.

$$\sqrt{3}\times \frac{1.985092303282644\sqrt{3}}{3}$$

Divide 1.985092303282644\sqrt{3} by 3 to get 0.661697434427548\sqrt{3}.

$$\sqrt{3}\times 0.661697434427548\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\times 0.661697434427548$$

Multiply 3 and 0.661697434427548 to get 1.985092303282644.

$$1.985092303282644$$