Question

find the length of side x. round to the nearest tenth.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 29\), \(b = 36\), \(C=40^{\circ}\), and we want to find \(x\).
So, \(x^{2}=29^{2}+36^{2}-2\times29\times36\times\cos40^{\circ}\).
First, calculate \(29^{2}=841\), \(36^{2} = 1296\), and \(\cos40^{\circ}\approx0.7660\).
Then \(2\times29\times36=2088\).

Step2: Substitute values into the formula

\(x^{2}=841 + 1296-2088\times0.7660\).
\(x^{2}=841+1296 - 1600.408\).
\(x^{2}=2137-1600.408\).
\(x^{2}=536.592\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{536.592}\approx23.2\).

Answer:

\(23.2\)