Chapter 5.6, Problem 45E

Solution

To find: Whether the given statement is true and false.

The given statement is true.

Given information:

The given statement says that in $\Delta ABC$, $b^2+c^2>2(b)(c)\cos A$ .

Formula used:

Law of Cosine

  $b^2+c^2-2(b)(c)\cos A=a^2$

Calculation:

Consider the law of cosine for $\Delta ABC$

  $b^2+c^2-2(b)(c)\cos A=a^2$

Side $a$ of the triangle needs to be greater than zero so that the triangle exits.

  $b^2+c^2-2(b)(c)\cos A>0$

Add $2(b)(c)\cos A$ to both sides.

  $b^2+c^2>2(b)(c)\cos A$

Therefore, the given statement is true.