Question

•cos(x)
17
11
x°
10

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In the given triangle, let \(a = 10\), \(b = 11\), \(c = 17\), and \(C=x\). Then \(17^{2}=10^{2}+11^{2}-2\times10\times11\times\cos x\).

Step2: Simplify the equation

First, calculate the squares: \(289 = 100 + 121-220\cos x\). Then \(289=221 - 220\cos x\).

Step3: Solve for \(\cos x\)

Rearrange the equation: \(220\cos x=221 - 289\). So \(220\cos x=- 68\). Then \(\cos x=\frac{-68}{220}=-\frac{17}{55}\).

Step4: Find \(x\)

\(x=\cos^{-1}(-\frac{17}{55})\approx108.1^{\circ}\)

Answer:

\(x\approx108.1^{\circ}\)