Question

what does the law of cosines reduce to when dealing with a right triangle?
a. the law of sines
b. the formula for a triangles area
c. the pythagorean theorem
d. the law of cosines cannot be applied to a right triangle.

Explanation:

Step1: Recall law of cosines

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

Step2: Consider right - triangle

In a right - triangle, if \(C = 90^{\circ}\), then \(\cos C=\cos90^{\circ}=0\).

Step3: Simplify law of cosines

Substituting \(\cos C = 0\) into the law of cosines formula \(c^{2}=a^{2}+b^{2}-2ab\cos C\), we get \(c^{2}=a^{2}+b^{2}\), which is the Pythagorean theorem.

Answer:

C. The Pythagorean theorem