Question

the law of cosines reduces to the pythagorean theorem whenever the triangle is acute.
a. true
b. false

Explanation:

Step1: Recall the law of cosines

The law of cosines is \(c^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a\), \(b\), \(c\) are the sides of the triangle and \(C\) is the angle opposite to side \(c\).

Step2: Analyze when it reduces to Pythagorean theorem

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). This happens when \(\cos C = 0\), i.e., \(C = 90^{\circ}\) (right - angled triangle), not when the triangle is acute (\(0^{\circ}0\)).

Answer:

B. False