Solve 100+htan(47)=htan(54)

$$100+h \tan ( 47 ) = h \tan ( 54 )$$

Solve for h_1

$$h_{1} = \frac{250000000000000000}{760033026116227} = 328\frac{709167433877544}{760033026116227} \approx 328.933074497$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$100 + h 1.0723687100246826 = h 1.3763819204711734$$

Subtract h_{1}\times 0.3763819204711734 from both sides.

$$100+h_{1}\times 0.0723687100246826-h_{1}\times 0.3763819204711734=0$$

Combine h_{1}\times 0.0723687100246826 and -h_{1}\times 0.3763819204711734 to get -0.3040132104464908h_{1}.

$$100-0.3040132104464908h_{1}=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-0.3040132104464908h_{1}=-100$$

Divide both sides by -0.3040132104464908.

$$h_{1}=\frac{-100}{-0.3040132104464908}$$

Expand \frac{-100}{-0.3040132104464908} by multiplying both numerator and the denominator by 10000000000000000.

$$h_{1}=\frac{-1000000000000000000}{-3040132104464908}$$

Reduce the fraction \frac{-1000000000000000000}{-3040132104464908} to lowest terms by extracting and canceling out -4.

$$h_{1}=\frac{250000000000000000}{760033026116227}$$