Question

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

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(v^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 12\), \(b = 20\), and \(C=43^{\circ}\).
So, \(v^{2}=12^{2}+20^{2}-2\times12\times20\times\cos(43^{\circ})\).
First, calculate \(12^{2}=144\), \(20^{2} = 400\), and \(2\times12\times20=480\).
\(\cos(43^{\circ})\approx0.7314\).
Then \(v^{2}=144 + 400-480\times0.7314\).

Step2: Calculate the value of \(v^{2}\)

\(144+400=544\).
\(480\times0.7314 = 351.072\).
\(v^{2}=544-351.072=192.928\).

Step3: Find the value of \(v\)

Take the square - root of \(v^{2}\), \(v=\sqrt{192.928}\approx13.9\).

Answer:

\(13.9\)