Chapter 14, Problem 3CV

Solution

To complete: the given sentence.

If you know the measures of two sides and the angle between them, you can use Law of Cosines to find missing parts of any triangle.

Given:

If you know the measures of two sides and the angle between them, you can use _____ to find missing parts of any triangle.

Concept used:

Law of Cosines:

In a triangle ABC, let $a,b$ , and $c$ represents the length of the sides opposite $\angle A,\angle B$ , and $\angle C$ , respectively. Then,

  $\begin{array}{l}{a}^2=b^2+c^2-2bc\cos A\\ b^2=a^2+c^2-2ac\cos B\\ c^2=a^2+b^2-2ab\cos C\end{array}$ .

Calculation:

If the measure of two sides and an angle between them are given, then the Law of Cosines can be used to find the missing measures of the triangle.

Therefore, if you know the measures of two sides and the angle between them, you can use Law of Cosines to find missing parts of any triangle.