Resol 5/sin48^circ65/sin45^circ

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

Calcula

$$\frac{3250000000000000000\sqrt{2}}{7431448254773941}\approx 618,478918259$$

Passos de solució

Evaluate trigonometric functions in the problem

$$\frac{5}{0,7431448254773941} \frac{65}{\sin(45)}$$

Amplieu \frac{5}{0,7431448254773941} multiplicant tant el numerador com el denominador per 10000000000000000.

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

Obteniu el valor de \sin(45) de la taula de valors trigonomètrics.

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

Dividiu 65 per \frac{\sqrt{2}}{2} multiplicant 65 pel recíproc de \frac{\sqrt{2}}{2}.

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

Racionalitzeu el denominador de \frac{65\times 2}{\sqrt{2}} multiplicant el numerador i el denominador per \sqrt{2}.

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

L'arrel quadrada de \sqrt{2} és 2.

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

Multipliqueu 65 per 2 per obtenir 130.

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

Dividiu 130\sqrt{2} entre 2 per obtenir 65\sqrt{2}.

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

Multipliqueu \frac{50000000000000000}{7431448254773941} per 65 per obtenir \frac{3250000000000000000}{7431448254773941}.

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