Solve 20sin45^circ/sin75^circ

$$\frac { 20 \sin 45 ^ { \circ } } { \sin 75 ^ { \circ } }$$

Evaluate

$$\frac{100000000000000000\sqrt{2}}{9659258262890683}\approx 14.641016151$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{20 \sin(45)}{0.9659258262890683}$$

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

$$\frac{20\times \frac{\sqrt{2}}{2}}{0.9659258262890683}$$

Cancel out 2, the greatest common factor in 20 and 2.

$$\frac{10\sqrt{2}}{0.9659258262890683}$$

Divide 10\sqrt{2} by 0.9659258262890683 to get \frac{100000000000000000}{9659258262890683}\sqrt{2}.

$$\frac{100000000000000000}{9659258262890683}\sqrt{2}$$