Question

17
in △abc,m∠a = 60°. what is a²?
b² + c² - bc
b² - c² + 2bc cos b
b² - c² - 2bc
b² + c² - 2bc cos b

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle \(ABC\) with sides \(a\), \(b\), \(c\) and angle \(A\) opposite side \(a\), \(a^{2}=b^{2}+c^{2}-2bc\cos A\).

Step2: Substitute the value of \(\cos A\)

Given \(m\angle A = 60^{\circ}\), and \(\cos60^{\circ}=\frac{1}{2}\).
Substituting \(\cos A=\frac{1}{2}\) into the Law - of - Cosines formula:

$$
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Answer:

A. \(b^{2}+c^{2}-bc\)