Resolver 5/sin48^circ65/sin45^circ

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

Calcular

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

Pasos da solución

Evaluate trigonometric functions in the problem

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

Expande \frac{5}{0.7431448254773941} multiplicando o numerador e o denominador por 10000000000000000.

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

Obtén o valor de \sin(45) a partir da táboa de valores trigonométricos.

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

Divide 65 entre \frac{\sqrt{2}}{2} mediante a multiplicación de 65 polo recíproco de \frac{\sqrt{2}}{2}.

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

Racionaliza o denominador de \frac{65\times 2}{\sqrt{2}} mediante a multiplicación do numerador e o denominador por \sqrt{2}.

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

O cadrado de \sqrt{2} é 2.

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

Multiplica 65 e 2 para obter 130.

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

Divide 130\sqrt{2} entre 2 para obter 65\sqrt{2}.

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

Multiplica \frac{50000000000000000}{7431448254773941} e 65 para obter \frac{3250000000000000000}{7431448254773941}.

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