Question

question 1 of 10
what does the law of cosines reduce to when dealing with a right triangle?
a. the formula for a triangles area
b. the pythagorean theorem
c. the law of cosines cannot be applied to a right triangle.
d. the law of sines

Explanation:

Step1: Recall the law of cosines formula

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

Step2: Consider a right - triangle

In a right - triangle, if \(C = 90^{\circ}\), then \(\cos C=\cos90^{\circ}=0\).
Substituting \(\cos C = 0\) into the law of cosines formula \(c^{2}=a^{2}+b^{2}-2ab\cos C\), we get \(c^{2}=a^{2}+b^{2}-2ab\times0=a^{2}+b^{2}\).

Answer:

B. The Pythagorean theorem