Law of Sines and the Ambiguous Case
Problem: In ∆FQG, f = 12, q = 10, and m<F = 75º.
How many distinct triangles can be drawn given these measurements?
Solution Use the Law of Sines:
Step 1: f / sin F = q / sin Q
Solution 12/sin75° = 10 / sin Q
Solution 12(sin Q) = 10 * sin75°
Solution sin Q = 10 * (1)/12 = 0.8
Step 4: Angles could be 75º, 53.1º, and 51.9º: sum 180º
But, with m<F = 75º and m<Q = 53.1º the sum of the angles
would exceed 180º.Not possible! Therefore, m<Q = 51.9º, m<f = 75º,
and m<Q = 53.1º and only ONE triangle is possible.
Solution Answer: only ONE triangle is possible.
Try two practice problems:
Solve the following:
From the Above Diagram solve the following: