Question

find the length of side x. round to the nearest tenth.
16
40°
20
x
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Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 16\), \(b = 20\), and \(C=40^{\circ}\).
So, \(x^{2}=16^{2}+20^{2}-2\times16\times20\times\cos40^{\circ}\).

Step2: Calculate each term

First, \(16^{2}=256\), \(20^{2} = 400\).
\(\cos40^{\circ}\approx0.7660\).
\(2\times16\times20\times0.7660=2\times320\times0.7660 = 640\times0.7660=490.24\).
Then \(x^{2}=256 + 400-490.24\).

Step3: Simplify the right - hand side

\(x^{2}=656-490.24=165.76\).

Step4: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{165.76}\approx12.9\).

Answer:

\(12.9\)