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

User Ben Hamner
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1 Answer

17 votes
17 votes

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.

If A=30° b=40 ft, a=10ft explain why this triangle has no solution-example-1
User John Kline Kurtz
by
3.1k points
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