Resolver 5/sin48^circ65/sin45^circ

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

Avaliar

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

Passos Para a Resolução

Evaluate trigonometric functions in the problem

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

Expanda \frac{5}{0,7431448254773941} ao multiplicar o numerador e o denominador por 10000000000000000.

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

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

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

Divida 65 por \frac{\sqrt{2}}{2} ao multiplicar 65 pelo recíproco de \frac{\sqrt{2}}{2}.

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

Racionalize o denominador de \frac{65\times 2}{\sqrt{2}} ao multiplicar o numerador e o denominador por \sqrt{2}.

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

O quadrado de \sqrt{2} é 2.

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

Multiplique 65 e 2 para obter 130.

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

Dividir 130\sqrt{2} por 2 para obter 65\sqrt{2}.

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

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

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