Chapter 12.4, Problem 9CYU

To determine

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

Answer to Problem 9CYU

No solution.

Explanation of Solution

Given information:

  $\begin{array}{l}A={60}^0\\ a=15\\ b=24\end{array}$

Given

  $\begin{array}{l}A={60}^0\\ a=15\\ b=24\end{array}$

Here $A={60}^0$ is Acute angle.

Because A is Acute and $15<24$ that is $a<b$

Now we need to find $h$ and compare it to $a$ .

We know

  $h=b\sin A$

On substituting values

We get

  $\begin{array}{l}h=b\sin A\\ \Rightarrow h=24\sin \left({60}^0\right)\\ \Rightarrow h=24\left(0.866\right)\\ \Rightarrow h=20.78\end{array}$

Therefore,

We got $a<h$

It means no Solution.