Question

how many triangles exist that fit the following criteria?
c = 125°, c = 5, b = 8

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\sin B}{b}=\frac{\sin C}{c}\). Substituting the given values \(C = 125^{\circ}\), \(c = 5\), and \(b = 8\), we get \(\sin B=\frac{b\sin C}{c}\).

$$ \sin B=\frac{8\sin125^{\circ}}{5} $$

$$ \sin B=\frac{8\times0.8192}{5}=\frac{6.5536}{5}=1.31072 $$

Step2: Analyze the value of \(\sin B\)

Since the range of the sine function is \([- 1,1]\), and \(\sin B = 1.31072>1\)

Answer:

\(0\)