This case, where you have 3 given sides and no given angles, requires the use of the cosine law. The cosine law is as follows:
\(a^{2} = b^{2} + c^{2} - 2bc\:cosA\)
Add your given values to the equation and simplify:
\(3^{2} = 5^{2} + 7^{2} -2(5)(7)cosA\)
\(9 = 25 + 49 - 70cosA\)
\(9 - 25 - 49 = -70cosA\)
\(-65 = -70cosA\)
\(cosA = \frac{-65}{-70}\)
\(cosA = \frac{13}{14}\)
\(A = cos^{-1}\:\frac{13}{14}\)
Use your scientific calculator to evaluate. Round the answer to as many decimal places as the question asks:
\(A = 21.7867893...\:^{\circ}\)
Hope this helped :)
