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Question

# In this given problem using the Law of Cosines to solve the triangle.$\beta=100^{\circ}, a=22.3, b=16.1$

Solution

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First find the angle $\alpha$ using the Law of Sines:

\begin{aligned} \dfrac{\sin\alpha}{22.3}&=\dfrac{\sin100^\circ}{16.1}\\ \sin\alpha&=\dfrac{22.3\cdot\sin100^\circ}{16.1}\\ \sin\alpha&\approx1.36 \end{aligned}

Since the value of $\sin$ is less than $1$, we cannot find the angle $\alpha$. In that case, the triangle does not exist.

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