Chapter 12.4, Problem 48HP

To determine

To find: a value for $e$ such that no triangle DEF can exist.

Answer to Problem 48HP

  $e<33.6$

Explanation of Solution

Given information:

  $\begin{array}{l}E={62}^0\\ d=38\end{array}$

Given

  $\begin{array}{l}E={62}^0\\ d=38\end{array}$

Using law of sines

We get

  $\begin{array}{l}\frac{\sin D}{d}=\frac{\sin E}{e}\\ \Rightarrow \frac{\sin D}{38}=\frac{\sin {62}^0}{e}\\ \Rightarrow e=\frac{38\sin {62}^0}{\sin D}\\ \Rightarrow e=\frac{38\left(0.883\right)}{\sin D}\\ \Rightarrow e=\frac{33.6}{\sin D}\end{array}$

Since the value of $\sin D$ is between $0$ to $1$ , the value $e$ should be greater than or equal to $33.6$ .

For $e=30$ , the triangle will not exist.

For no triangle to exists, the length of the side opposite angle E must be less than $33.6$ to satisfy the Law of sines.

  $e<33.6$