Chapter 8.3, Problem 4AYU

To determine

To fill: The blank of the given statement.

Explanation of Solution

Given information:

The given statement is, “If one side and two angles of a triangle are given, the Law of ___________ is used to solve the triangle”.

Law of Cosines:

If ABC is a triangle with sides $a$ , $b$ , and $c$ , then

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

If only three sides of the triangle are known than the triangle is solved by using cosine rule.

For a triangle with sides a , b , c and opposite angles A , B , C , the Law of Sines state that

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

If one side and two angles of a triangle are given, the Law of Sine is used to solve the triangle

Thus, the blank of the given statement is filled with Sine.