Solve y^2+25^2-2*25ycos50^circ=125^2

$$y ^ { 2 } + 25 ^ { 2 } - 2 \times 25 y \cos 50 ^ { \circ } = 125 ^ { 2 }$$

Solve for y_0

$$y_{0}=\frac{100000000000000\left(y^{2}-15000\right)}{3213938048432697}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$y ^ {2} + 25 ^ {2} - 2 \cdot 25 y 0.6427876096865394 = 125 ^ {2}$$

Calculate 25 to the power of 2 and get 625.

$$y^{2}+625-2\times 25y_{0}\times 0.6427876096865394=125^{2}$$

Multiply 2 and 25 to get 50.

$$y^{2}+625-50y_{0}\times 0.6427876096865394=125^{2}$$

Multiply 50 and 0.6427876096865394 to get 32.13938048432697.

$$y^{2}+625-32.13938048432697y_{0}=125^{2}$$

Calculate 125 to the power of 2 and get 15625.

$$y^{2}+625-32.13938048432697y_{0}=15625$$

Subtract y^{2} from both sides.

$$625-32.13938048432697y_{0}=15625-y^{2}$$

Subtract 625 from both sides.

$$-32.13938048432697y_{0}=15625-y^{2}-625$$

Subtract 625 from 15625 to get 15000.

$$-32.13938048432697y_{0}=15000-y^{2}$$

Divide both sides of the equation by -32.13938048432697, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-32.13938048432697y_{0}}{-32.13938048432697}=\frac{15000-y^{2}}{-32.13938048432697}$$

Dividing by -32.13938048432697 undoes the multiplication by -32.13938048432697.

$$y_{0}=\frac{15000-y^{2}}{-32.13938048432697}$$

Divide 15000-y^{2} by -32.13938048432697 by multiplying 15000-y^{2} by the reciprocal of -32.13938048432697.

$$y_{0}=\frac{100000000000000y^{2}}{3213938048432697}-\frac{500000000000000000}{1071312682810899}$$

Solve for y

$$y=\frac{\sqrt{3213938048432697y_{0}+1500000000000000000}}{2}$$

$$y=-\frac{\sqrt{3213938048432697y_{0}+1500000000000000000}}{2}\text{, }y_{0}\geq -\frac{500000000000000000}{1071312682810899}$$