SOLUTION: what is the sine of an angle whose tangent is 2? first find an answer without a calculator, then check it with one. thank you!

Question 148692: what is the sine of an angle whose tangent is 2? first find an answer without a calculator, then check it with one.
thank you!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
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

Since Tan(x)=2, then
Opp/Adj = 2
Opp = 2 Adj
Opp/Hyp = 2 Adj/Hyp
Sin(x) = 2 Cos(x)

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,

From the calculator,
x=63.43
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