Solve 35/sin105^circ*frac{sqrt{2}}{2}

$$\frac { 35 } { \sin 105 ^ { \circ } } \times \frac { \sqrt { 2 } } { 2 }$$

Evaluate

$$\frac{175000000000000000\sqrt{2}}{9659258262890683}\approx 25.621778265$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{35}{0.9659258262890683} \cdot \frac{\sqrt{2}}{2}$$

Expand \frac{35}{0.9659258262890683} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{350000000000000000}{9659258262890683}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{350000000000000000}{9659258262890683} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{350000000000000000\sqrt{2}}{9659258262890683\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{175000000000000000\sqrt{2}}{9659258262890683}$$