Question

determine the number of triangles abc possible with the given parts. a = 32, b = 65, a = 79° a. 1 b. 2 c. 0 d. 3

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Substituting the given values \(a = 32\), \(b = 65\), and \(A=79^{\circ}\), we get \(\frac{32}{\sin79^{\circ}}=\frac{65}{\sin B}\). Then \(\sin B=\frac{65\sin79^{\circ}}{32}\).

Step2: Calculate \(\sin B\)

We know that \(\sin79^{\circ}\approx0.9816\). So \(\sin B=\frac{65\times0.9816}{32}\approx\frac{63.804}{32}\approx1.994\).

Step3: Analyze the value of \(\sin B\)

Since the range of the sine function is \([- 1,1]\), and \(1.994>1\), there is no angle \(B\) that satisfies the equation.

Answer:

C. 0