Solve ytan(40)=(13+y)tan(20)

$$y \tan ( 40 ) = (13+y) \tan ( 20 )$$

Solve for y

$$y=\frac{41954981558863995y_{0}}{18198511713310117}-13$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$y 0.8390996311772799 = {(13 + y)} 0.36397023426620234$$

Use the distributive property to multiply 13+y by 0.36397023426620234.

$$y_{0}\times 0.8390996311772799=4.73161304546063042+0.36397023426620234y$$

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

$$4.73161304546063042+0.36397023426620234y=y_{0}\times 0.8390996311772799$$

Subtract 4.73161304546063042 from both sides.

$$0.36397023426620234y=y_{0}\times 0.8390996311772799-4.73161304546063042$$

The equation is in standard form.

$$0.36397023426620234y=\frac{8390996311772799y_{0}}{10000000000000000}-4.73161304546063042$$

Divide both sides of the equation by 0.36397023426620234, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.36397023426620234y}{0.36397023426620234}=\frac{\frac{8390996311772799y_{0}}{10000000000000000}-4.73161304546063042}{0.36397023426620234}$$

Dividing by 0.36397023426620234 undoes the multiplication by 0.36397023426620234.

$$y=\frac{\frac{8390996311772799y_{0}}{10000000000000000}-4.73161304546063042}{0.36397023426620234}$$

Divide \frac{8390996311772799y_{0}}{10000000000000000}-4.73161304546063042 by 0.36397023426620234 by multiplying \frac{8390996311772799y_{0}}{10000000000000000}-4.73161304546063042 by the reciprocal of 0.36397023426620234.

$$y=\frac{41954981558863995y_{0}}{18198511713310117}-13$$

Solve for y_0

$$y_{0}=\frac{18198511713310117y+236580652273031521}{41954981558863995}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$y 0.8390996311772799 = {(13 + y)} 0.36397023426620234$$

Use the distributive property to multiply 13+y by 0.36397023426620234.

$$y_{0}\times 0.8390996311772799=4.73161304546063042+0.36397023426620234y$$

The equation is in standard form.

$$0.8390996311772799y_{0}=\frac{18198511713310117y+236580652273031521}{50000000000000000}$$

Divide both sides of the equation by 0.8390996311772799, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.8390996311772799y_{0}}{0.8390996311772799}=\frac{18198511713310117y+236580652273031521}{0.8390996311772799\times 50000000000000000}$$

Dividing by 0.8390996311772799 undoes the multiplication by 0.8390996311772799.

$$y_{0}=\frac{18198511713310117y+236580652273031521}{0.8390996311772799\times 50000000000000000}$$

Divide \frac{236580652273031521+18198511713310117y}{50000000000000000} by 0.8390996311772799 by multiplying \frac{236580652273031521+18198511713310117y}{50000000000000000} by the reciprocal of 0.8390996311772799.

$$y_{0}=\frac{18198511713310117y+236580652273031521}{41954981558863995}$$