Question

1. given the triangle below, find the measure of cb.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(CB^{2}=AC^{2}+AB^{2}-2(AC)(AB)\cos A\).
Given \(AC = 23\), \(AB=26\), and \(A = 114^{\circ}\), substitute these values into the formula:

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Step2: Calculate each term

First, \(23^{2}=529\), \(26^{2} = 676\).
\(\cos(114^{\circ})\approx - 0.4067\)

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Then \(CB^{2}=529 + 676-(-486.41)=529+676 + 486.41=1691.41\)

Step3: Find \(CB\)

Take the square root of \(CB^{2}\): \(CB=\sqrt{1691.41}\approx41.1\)

Answer:

\(CB\approx41.1\)