Question

in △abc, cosc = -0.2, a = 8, and b = 10. find the length of side c.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).

Step2: Substitute the given values

Given \(a = 8\), \(b = 10\), and \(\cos C=-0.2\).
Substitute into the formula:
\(c^{2}=8^{2}+10^{2}-2\times8\times10\times(-0.2)\)
\(c^{2}=64 + 100+32\)
\(c^{2}=196\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{196}\)

Answer:

\(14\)