Chapter 12.4, Problem 44HP

To determine

To find: How many triangles can be formed if $b=5$ .

Answer to Problem 44HP

Two triangles can be formed

Explanation of Solution

Given information:

  $\begin{array}{l}B={30}^0\\ a=6\\ b=5\end{array}$

Given

  $\begin{array}{l}B={30}^0\\ a=6\\ b=5\end{array}$

Here Angle B is acute

And $5<6$ it means $b<a$ .

Now we need to find the value of $h$ and compare it to $b$

We know

  $h=a\sin B$

On substituting values

We get

  $\begin{array}{l}h=a\sin B\\ \Rightarrow h=6\sin {30}^0\\ \Rightarrow h=6\left(0.5\right)\\ \Rightarrow h=3\end{array}$

We can say that

  $h<b<a$

Therefore,

As $h<b<a$ there will be two solutions.

So, two triangles can be formed.