Chapter 13, Problem 32SGR

To determine

To find: Whether each triangle has no solution, one solution or two solutions.

Answer to Problem 32SGR

There will be no solution.

Explanation of Solution

Given information:

  $\begin{array}{l}A={70}^0\\ a=5\\ c=16\end{array}$

Given

  $\begin{array}{l}A={70}^0\\ a=5\\ c=16\end{array}$

Here $A={70}^0$ is Acute angle.

Because A is Acute and $5<16$ that is $a<c$ .

We need to find $h$ and compare it with $a$ .

We know

  $h=c\sin A$

On substituting values

We get

  $\begin{array}{l}h=c\sin A\\ \Rightarrow h=16\sin {70}^0\\ \Rightarrow h=16\left(0.94\right)\\ \Rightarrow h=15\end{array}$

We got

  $a<h$

So, there will be no solution.

Therefore,

There will be no solution.