Solve 12*sin75^circ/sin60^circ

$$\frac { 12 \times \sin 75 ^ { \circ } } { \sin 60 ^ { \circ } }$$

Evaluate

$$\frac{9659258262890683\sqrt{3}}{1250000000000000}\approx 13.38426086$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{12 \cdot 0.9659258262890683}{\sin(60)}$$

Multiply 12 and 0.9659258262890683 to get 11.5911099154688196.

$$\frac{11.5911099154688196}{\sin(60)}$$

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

$$\frac{11.5911099154688196}{\frac{\sqrt{3}}{2}}$$

Divide 11.5911099154688196 by \frac{\sqrt{3}}{2} by multiplying 11.5911099154688196 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{11.5911099154688196\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{11.5911099154688196\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{11.5911099154688196\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{11.5911099154688196\times 2\sqrt{3}}{3}$$

Multiply 11.5911099154688196 and 2 to get 23.1822198309376392.

$$\frac{23.1822198309376392\sqrt{3}}{3}$$

Divide 23.1822198309376392\sqrt{3} by 3 to get 7.7274066103125464\sqrt{3}.

$$7.7274066103125464\sqrt{3}$$