Question

find q.
write your answer as an integer or as a decimal rounded to the nearest tenth.
q =
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Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( q^{2}=14^{2}+11^{2}-2\times14\times11\times\cos(113^{\circ})\).
First, calculate \(14^{2} = 196\), \(11^{2}=121\), and \(2\times14\times11 = 308\).
\(\cos(113^{\circ})\approx - 0.39073\).

Step2: Substitute values into the formula

\(q^{2}=196 + 121-308\times(-0.39073)\).
\(q^{2}=317+120.34584\).
\(q^{2}=437.34584\).

Step3: Solve for \(q\)

Take the square - root of both sides: \(q=\sqrt{437.34584}\approx20.9\).

Answer:

\(20.9\)