Solve 7sin21^circ/sqrt{3/2}

$$\frac { 7 \sin 21 ^ { \circ } } { \frac { \sqrt { 3 } } { 2 } }$$

Evaluate

$$\frac{250857564681710189\sqrt{3}}{150000000000000000}\approx 2.89665365$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{7 \cdot 0.35836794954530027}{\frac{\sqrt{3}}{2}}$$

Multiply 7 and 0.35836794954530027 to get 2.50857564681710189.

$$\frac{2.50857564681710189}{\frac{\sqrt{3}}{2}}$$

Divide 2.50857564681710189 by \frac{\sqrt{3}}{2} by multiplying 2.50857564681710189 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{2.50857564681710189\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{2.50857564681710189\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2.50857564681710189\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2.50857564681710189\times 2\sqrt{3}}{3}$$

Multiply 2.50857564681710189 and 2 to get 5.01715129363420378.

$$\frac{5.01715129363420378\sqrt{3}}{3}$$

Divide 5.01715129363420378\sqrt{3} by 3 to get \frac{250857564681710189}{150000000000000000}\sqrt{3}.

$$\frac{250857564681710189}{150000000000000000}\sqrt{3}$$