Chapter 5.8, Problem 3CFU

To determine

To explain: the given statement.

Answer to Problem 3CFU

See explanation.

Explanation of Solution

Given information:

The Pythagorean Theorem is a special case of the Law of Cosines.

Calculation:

This Pythagorean Theorem is linked to the law of the cosines as a special case. All triangles that have one right angle are special cases of the law of cosines. The law of cosines is as follows: $a^2+b^2-2\cdot a\cdot b\cdot \cos \theta =c^2$

Here $\theta$ is the angle between the two sides $a\text{ and }b$ . In case of right-angle triangle $\theta =90°$ .

Put the value of in the above equation and simplify it as shown below.

  $\begin{array}{c}{a}^2+b^2-2\cdot a\cdot b\cdot \cos 90°=c^2\\ a^2+b^2-2\cdot a\cdot b\cdot \left(0\right)=c^2\\ a^2+b^2=c^2\end{array}$

Thus, the Pythagorean Theorem is a special case of the Law of Cosines.