Question 148692
From trigonometry, you know the following identities, where
Opp = Length of triangle leg opposite to angle x.
Adj = Length of triangle leg adjacent to angle x.
Hyp = Hypotenuse of triangle with sides Opp and Adj.
Tan(x)=Opp/Adj
Sin(x)=Opp/Hyp
Cos(x)=Adj/Hyp
{{{Sin^2(x)+Cos^2(x)=1}}}
Since Tan(x)=2, then
Opp/Adj = 2
Opp = 2 Adj
Opp/Hyp = 2 Adj/Hyp
Sin(x) = 2 Cos(x)
{{{(2 Cos(x))^2+Cos^2(x)=1}}}
{{{4*Cos^2(x)+Cos^2(x)=1}}}
{{{5*Cos^2(x)=1}}}
{{{Cos^2(x)=1/5}}}
{{{Cos(x)=1/sqrt(5)}}}
{{{Cos(x)=.4472}}}
Checking the sine tables, 
0.4478 for 63.4
0.4462 for 63.5
We can set up a proportion to get an approximate answer,
{{{(63.4-x)/(63.4-63.5)=(0.4478-0.4472)/(0.4478-0.4462)}}}
{{{(63.4-x)/(-0.1)=(0.0006)/(0.0016)}}}
{{{63.4-x=-.0375}}}
{{{x=63.44}}}
From the calculator,
x=63.43