Final answer:
To find the value of cos e, we can use the law of cosines by plugging in the given side lengths into the formula c^2 = a^2 + b^2 - 2ab * cos e and solving for cos e.
Step-by-step explanation:
To use the law of cosines to find the value of cos e, we need to use the formula: c^2 = a^2 + b^2 - 2ab * cos e. In this case, the sides given are a = 5.7, b = 10.2, and c = 9.8. Plugging in these values into the formula, we can solve for cos e:
9.8^2 = 5.7^2 + 10.2^2 - 2 * 5.7 * 10.2 * cos e
Simplifying the equation:
96.04 = 32.49 + 104.04 - 116.28 * cos e
Subtracting 32.49 and 104.04 from both sides:
-40.49 = -116.28 * cos e
Dividing both sides by -116.28:
cos e = -40.49 / -116.28 = 0.3484