Solve 7sin39^circ/sqrt{3/2}

$$\frac { 7 \sin 39 ^ { \circ } } { \frac { \sqrt { 3 } } { 2 } }$$

Evaluate

$$\frac{22026213686744309\sqrt{3}}{7500000000000000}\approx 5.086736161$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{7 \cdot 0.6293203910498374}{\frac{\sqrt{3}}{2}}$$

Multiply 7 and 0.6293203910498374 to get 4.4052427373488618.

$$\frac{4.4052427373488618}{\frac{\sqrt{3}}{2}}$$

Divide 4.4052427373488618 by \frac{\sqrt{3}}{2} by multiplying 4.4052427373488618 by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{4.4052427373488618\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{4.4052427373488618\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4.4052427373488618\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4.4052427373488618\times 2\sqrt{3}}{3}$$

Multiply 4.4052427373488618 and 2 to get 8.8104854746977236.

$$\frac{8.8104854746977236\sqrt{3}}{3}$$

Divide 8.8104854746977236\sqrt{3} by 3 to get \frac{22026213686744309}{7500000000000000}\sqrt{3}.

$$\frac{22026213686744309}{7500000000000000}\sqrt{3}$$