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:
[tex] a^{2} = b^{2} + c^{2} - 2bc\:cosA[/tex]
Add your given values to the equation and simplify:
[tex]3^{2} = 5^{2} + 7^{2} -2(5)(7)cosA[/tex]
[tex]9 = 25 + 49 - 70cosA[/tex]
[tex]9 - 25 - 49 = -70cosA[/tex]
[tex]-65 = -70cosA[/tex]
[tex]cosA = \frac{-65}{-70}[/tex]
[tex]cosA = \frac{13}{14}[/tex]
[tex]A = cos^{-1}\:\frac{13}{14}[/tex]
Use your scientific calculator to evaluate. Round the answer to as many decimal places as the question asks:
[tex]A = 21.7867893...\:^{\circ}[/tex]
Hope this helped :)
