Chapter 6.1, Problem 56E

To determine

Whether the given statement is true or false and then justify.

Answer to Problem 56E

The given statement is false.

Explanation of Solution

Given:

Two angles and one side of the triangles do not necessarily determine a unique triangle.

Considering the triangle:

  

Referring to the above figure, the angle A,B and C and the sides are a,b and c which are opposite to them.

Considering that two angles B and C are provide with the side length a.

Hence, the third angle A can be determined from the equation:

  $A={180}^o-\left(B+C\right)$

According to the law of sin:

If the ABC is the triangle with the sides a,b and c opposite to the angle A,B and C respectively.

Then,

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

From the above expression all the angles are known and the side a is known. The unknown parameters are b and c and it can be evaluated by the above expression.

Therefore, the given statement is false.