Solve 5/sin48^circ65/sin45^circ

$$\frac { 5 } { \sin 48 ^ { \circ } } \frac { 65 } { \sin 45 ^ { \circ } }$$

Evaluate

$$\frac{3250000000000000000\sqrt{2}}{7431448254773941}\approx 618.478918259$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5}{0.7431448254773941} \frac{65}{\sin(45)}$$

Expand \frac{5}{0.7431448254773941} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{50000000000000000}{7431448254773941}\times \frac{65}{\sin(45)}$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{50000000000000000}{7431448254773941}\times \frac{65}{\frac{\sqrt{2}}{2}}$$

Divide 65 by \frac{\sqrt{2}}{2} by multiplying 65 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{50000000000000000}{7431448254773941}\times \frac{65\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{65\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{50000000000000000}{7431448254773941}\times \frac{65\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{50000000000000000}{7431448254773941}\times \frac{65\times 2\sqrt{2}}{2}$$

Multiply 65 and 2 to get 130.

$$\frac{50000000000000000}{7431448254773941}\times \frac{130\sqrt{2}}{2}$$

Divide 130\sqrt{2} by 2 to get 65\sqrt{2}.

$$\frac{50000000000000000}{7431448254773941}\times 65\sqrt{2}$$

Multiply \frac{50000000000000000}{7431448254773941} and 65 to get \frac{3250000000000000000}{7431448254773941}.

$$\frac{3250000000000000000}{7431448254773941}\sqrt{2}$$