The Law of Cosines tells us that, given any triangle ABC:
Then:
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
In this case:
a = 21
b = 23
c = 17
By the Law of Cosines:
[tex]21^2=23^2+17^2-2\cdot23\cdot17\cdot\cos(A)[/tex]
And solve:
[tex]\begin{gathered} 441=529+289-782\cos(A) \\ . \\ 441-818=-782\cos(A) \\ . \\ \frac{-377}{-782}=\cos(A) \end{gathered}[/tex]
Now we can apply arc cosine on both sides:
[tex]A=\cos^{-1}(\frac{377}{782})\approx61.1775[/tex]
The answer is, to one accurate decimal place:
A = 61.18 degrees.
