Find the length of a to the nearest tenth.
We can use the Law of Cosines here
a^2 = 7^2 + 9^2 - 2(7)(9)cos(46°)
a^2 = 49 + 81 - 126(.695)
a^2 = 42.43 ......take the square root of both sides
a = about 6.5
Since the triangle is a SAS situation, use the Law of Cosines: b = 9 c = 7
a² = b² + c² - 2·b·c·cosA
a² = 9² + 7² - 2·9·7·cos46
a² = 42.473
a = 6.5