Question

determine the number of triangles abc possible with the given parts.
a = 35, b = 71, a = 71°

a. 2
b. 1
c. 3
d. 0

Explanation:

Step1: Apply the sine rule

The sine rule states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Substituting the given values \(a = 35\), \(b = 71\), and \(A=71^{\circ}\), we get \(\frac{35}{\sin71^{\circ}}=\frac{71}{\sin B}\).

Step2: Solve for \(\sin B\)

Cross - multiplying gives \(35\sin B=71\sin71^{\circ}\). Then \(\sin B=\frac{71\sin71^{\circ}}{35}\).
Calculate \(\sin71^{\circ}\approx0.9455\), so \(\sin B=\frac{71\times0.9455}{35}\approx\frac{67.1305}{35}\approx1.918\).

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

Since the range of the sine function is \([- 1,1]\), and \(\sin B\approx1.918>1\), no such angle \(B\) exists.

Answer:

D. 0