Solve 5sin10=pix^2

$$5 \sin 10 = \pi x ^ { 2 }$$

Solve for x

$$x=\frac{\sqrt{\frac{34729635533386066}{\pi }}}{200000000}\approx 0.52570872$$

$$x=-\frac{\sqrt{\frac{34729635533386066}{\pi }}}{200000000}\approx -0.52570872$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$5 \cdot 0.17364817766693033 = \pi x ^ {2}$$

Multiply 5 and 0.17364817766693033 to get 0.86824088833465165.

$$0.86824088833465165=\pi x^{2}$$

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

$$\pi x^{2}=0.86824088833465165$$

Divide both sides by \pi .

$$\frac{\pi x^{2}}{\pi }=\frac{0.86824088833465165}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$x^{2}=\frac{0.86824088833465165}{\pi }$$

Divide 0.86824088833465165 by \pi .

$$x^{2}=\frac{17364817766693033}{20000000000000000\pi }$$

Take the square root of both sides of the equation.

$$x=\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }} x=-\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$5 \cdot 0.17364817766693033 = \pi x ^ {2}$$

Multiply 5 and 0.17364817766693033 to get 0.86824088833465165.

$$0.86824088833465165=\pi x^{2}$$

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

$$\pi x^{2}=0.86824088833465165$$

Subtract 0.86824088833465165 from both sides.

$$\pi x^{2}-0.86824088833465165=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -0.86824088833465165 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\pi \left(-0.86824088833465165\right)}}{2\pi }$$

Square 0.

$$x=\frac{0±\sqrt{-4\pi \left(-0.86824088833465165\right)}}{2\pi }$$

Multiply -4 times \pi .

$$x=\frac{0±\sqrt{\left(-4\pi \right)\left(-0.86824088833465165\right)}}{2\pi }$$

Multiply -4\pi times -0.86824088833465165.

$$x=\frac{0±\sqrt{\frac{17364817766693033\pi }{5000000000000000}}}{2\pi }$$

Take the square root of \frac{17364817766693033\pi }{5000000000000000}.

$$x=\frac{0±\frac{\sqrt{34729635533386066\pi }}{100000000}}{2\pi }$$

Now solve the equation x=\frac{0±\frac{\sqrt{34729635533386066\pi }}{100000000}}{2\pi } when ± is plus.

$$x=\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }}$$

Now solve the equation x=\frac{0±\frac{\sqrt{34729635533386066\pi }}{100000000}}{2\pi } when ± is minus.

$$x=-\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }}$$

The equation is now solved.

$$x=\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }} x=-\frac{17364817766693033}{100000000\sqrt{34729635533386066\pi }}$$