Although the Law of Sines can be used to solve oblique triangles, there may be cases that would give us one triangle, two triangles, or even no solution. Such cases are known as the
ambiguous case. This occurs when we know two sides and an angle that is opposite to one of the given sides.
Example 4.1.8. Using Law of Sines (SSA) one-solution.
We can now return to the example at the start of the section where the Alingano Maisu must account for a current and we had the following triangle
What house do we need to head in order to account for current?
Solution.
Referring to
Table 4.1.7, our known angle (
) is acute, the side opposite of our angle (
) is greater than the side adjacent to the angle (
) so we have Case 4 and know that we have one triangle.
Using the first form of the Law of Sines
Taking the inverse sine we get
Now that we know the value of
we will need to add that to the heading that we determined in the last section (
) to get
Next we refer to the Star Compass with angles (
Figure 1.2.4) to conclude we will need to sail towards the House Noio Kona.