Chapter 7 - Section 7.2 - The Law of Cosines - 7.2 Problem Set - Page 378: 15

$a = 9.4$ m

$a^{2} = b^{2} + c^{2} - 2bccos(A)$ $a^{2} = (4.2)^{2} + (6.8)^{2} - 2(4.2)(6.8)cos(116)$ $a^{2} = 63.88 - 57.12cos(116)$ $a^{2} = 63.88 - (-25.0397599)$ $a^{2} = 88.9197....$ $a = \sqrt {88.9197...}$ by GDC / calculator $a = 9.429727...$ m $a = 9.4$ m