Chapter 11, Problem 9STP

To determine

To find: Which of the following equations can be used to solve for c in the given triangle.

1. $\frac{{10}^2}{\sin 25°}=\frac{c}{\sin 115°}$
2. $\frac{6.575}{\sin 115°}=\frac{c}{\sin 25°}$
3. $\frac{14.1}{\sin 40°}=\frac{c}{\sin 25°}$
4. $\frac{10}{\sin 40°}=\frac{c}{\sin 115°}$

Answer to Problem 9STP

 (D) $\frac{10}{\sin 40°}=\frac{c}{\sin 115°}$ can be used to solve for c .

Explanation of Solution

Given information: Given triangle is shown below figure.

  

Formula used:

In a triangle, the relationship between the length of sides and angle is:

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

Calculation:

In the given triangle:

  $b=10,\angle B={180}^{\circ }-({115}^{\circ }+{25}^{\circ })={40}^{\circ },\angle C={115}^{\circ }$

Hence, in the given triangle:

  $\begin{array}{l}\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{10}{\sin {40}^{\circ }}=\frac{c}{\sin {115}^{\circ }}\end{array}$

Therefore:

 (E) $\frac{10}{\sin 40°}=\frac{c}{\sin 115°}$ can be used to solve for c .