Solve 906=(6,30^2)x-2800sinθ

$$906 = ( 6,30 ^ { 2 } ) x - 2800 \sin \theta$$

Solve for x

$$x=\frac{1400\sin(\theta )+453}{2700}$$

Steps for Solving Linear Equation

Calculate 30 to the power of 2 and get 900.

$$906=6\times 900x-2800\sin(\theta )$$

Multiply 6 and 900 to get 5400.

$$906=5400x-2800\sin(\theta )$$

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

$$5400x-2800\sin(\theta )=906$$

Add 2800\sin(\theta ) to both sides.

$$5400x=906+2800\sin(\theta )$$

The equation is in standard form.

$$5400x=2800\sin(\theta )+906$$

Divide both sides by 5400.

$$\frac{5400x}{5400}=\frac{2\left(1400\sin(\theta )+453\right)}{5400}$$

Dividing by 5400 undoes the multiplication by 5400.

$$x=\frac{2\left(1400\sin(\theta )+453\right)}{5400}$$

Divide 2\left(453+1400\sin(\theta )\right) by 5400.

$$x=\frac{1400\sin(\theta )+453}{2700}$$

Solve for θ

$$\theta =\arcsin(\frac{3\left(151-900x\right)}{1400})+2\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}$$

$$\theta =-\arcsin(\frac{3\left(151-900x\right)}{1400})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }x\geq -\frac{947}{2700}\text{ and }x\leq \frac{1853}{2700}$$