Question

question 14 of 25 the law of cosines reduces to the pythagorean theorem whenever the triangle is acute. a. true b. false

Explanation:

Step1: Recall law of cosines

$c^{2}=a^{2}+b^{2}-2ab\cos C$

Step2: Recall Pythagorean theorem

$c^{2}=a^{2}+b^{2}$

Step3: Analyze when law of cosines becomes Pythagorean

The law of cosines $c^{2}=a^{2}+b^{2}-2ab\cos C$ reduces to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$ when $\cos C = 0$, which means $C = 90^{\circ}$ (right - angled triangle), not when the triangle is acute.

Answer:

B. False