Solve frac{10sqrt{2}}{1/2}=c/sin75^circ

$$\frac { 10 \sqrt { 2 } } { \frac { 1 } { 2 } } = \frac { c } { \sin 75 ^ { \circ } }$$

Solve for c

$$c = \frac{9659258262890683 \sqrt{2}}{500000000000000} = 27\frac{160254037844390}{500000000000000} \approx 27.320508076$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{10 \sqrt{2}}{\frac{1}{2}} = \frac{c}{0.9659258262890683}$$

Divide 10\sqrt{2} by \frac{1}{2} to get 20\sqrt{2}.

$$20\sqrt{2}=\frac{c}{0.9659258262890683}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{c}{0.9659258262890683}=20\sqrt{2}$$

The equation is in standard form.

$$\frac{10000000000000000}{9659258262890683}c=20\sqrt{2}$$

Divide both sides of the equation by \frac{10000000000000000}{9659258262890683}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{10000000000000000}{9659258262890683}c}{\frac{10000000000000000}{9659258262890683}}=\frac{20\sqrt{2}}{\frac{10000000000000000}{9659258262890683}}$$

Dividing by \frac{10000000000000000}{9659258262890683} undoes the multiplication by \frac{10000000000000000}{9659258262890683}.

$$c=\frac{20\sqrt{2}}{\frac{10000000000000000}{9659258262890683}}$$

Divide 20\sqrt{2} by \frac{10000000000000000}{9659258262890683} by multiplying 20\sqrt{2} by the reciprocal of \frac{10000000000000000}{9659258262890683}.

$$c=\frac{9659258262890683\sqrt{2}}{500000000000000}$$