Chapter 6.2, Problem 66E

a.

To determine

To describe:The appropriateformula (cosine or sine) to be used to solve the given triangle.

Answer to Problem 66E

To solve the given triangle the cosine formula should be used.

Explanation of Solution

Given:

The given triangle is shown in figure here.

Formula/ concept used:

The cosine formula is for the triangle ABC is $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Since, all sides of the triangle are given, therefore, the triangle can be solved using cosine formulae.

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$ , $\cos B=\frac{a^2+c^2-b^2}{2ac}$ , and $\cos C=\frac{a^2+b^2-c^2}{2ab}$

Conclusion:

To solve the given triangle the cosine formula should be used.

b.

To determine

To describe:The appropriateformula (cosine or sine) to be used to solve the given triangle.

Answer to Problem 66E

To solve the given triangle the sine formula should be used.

Explanation of Solution

Given:

The given triangle is shown in figure here.

Formula/ concept used:

The sine formula is for the triangle ABC is $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Description:

Since, one of sides of the triangle and its opposite angle is given, therefore, the triangle can be solved using sine formulae.

  $\frac{a}{\sin A}=\frac{18}{\sin {35}^0}=\frac{b}{\sin {55}^0}=\frac{c}{\sin {90}^0}$

Therefore, to solve the given triangle the sine formula should be used.