Question

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.​

Answer 1

Answer: 2

Explanation:

By the law of sines,

`(\sin B)/(b)=(\sin A)/(a) \\ \\ (\sin B)/(14)=(\sin 30^(\circ))/(8) \\ \\ (\sin B)/(14)=(1)/(16) \\ \\ \sin B=(14)/(16) \\ \\ B=\sin^(-1) \left((14)/(16) \right), 180^(\circ)-\sin^(-1) \left((14)/(16) \right) \\ \\ B \approx 61.04^(\circ), 118.96^(\circ)`

Since either of these values for B will form a triangle (as A+B will be less than 180 degrees), 2 triangles can be formed with these measurements.