Question

practice problem solve for $mangle b$

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle ABC\), if we want to find \(\angle B\), let \(a = 15\), \(c=10\), \(b = 12\). Then \(AC^{2}=AB^{2}+BC^{2}-2(AB)(BC)\cos B\). Substituting the values: \(15^{2}=12^{2}+10^{2}-2\times12\times10\times\cos B\).

Step2: Simplify the equation

$$
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$$

Step3: Solve for \(\cos B\)

\(\cos B=\frac{19}{240}\approx0.0792\)

Step4: Find the angle \(B\)

\(B=\cos^{-1}(0.0792)\approx85.5^{\circ}\)

Answer:

\(m\angle B\approx85.5^{\circ}\)