Question

If A=30° b=40 ft, a=10ft explain why this triangle has no solution

Answer 1

Given:

`A=30^(\circ),b=40ft,a=10ft`

The triangle is constructed as

Use the law of sine,

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c) \\ (\sin30^(\circ))/(10)=(\sin B)/(40)=(\sin C)/(c) \\ \text{Take,}(\sin30^(\circ))/(10)=(\sin B)/(40) \\ \sin B=(40)/(10)\cdot(1)/(2) \\ \sin B=2 \end{gathered}`

As, we know that,

`\begin{gathered} -1\leq\sin x\leq1 \\ It\text{ gives, }\sin B=2\text{ has no solution} \end{gathered}`

So, the given triangle can not be constructed.

Hence, the given triangle has no solution.