## How do you solve the sine ambiguous case?

Table of Contents

## How do you solve the sine ambiguous case?

The Ambiguous Case of the Law of Sines

- See if you are given two sides and the angle not in between (SSA).
- Find the value of the unknown angle.
- Once you find the value of your angle, subtract it from 180° to find the possible second angle.
- Add the new angle to the original angle.

## How many possible answers are there in the ambiguous case of the law of sines?

There are six different scenarios related to the ambiguous case of the Law of sines: three result in one triangle, one results in two triangles and two result in no triangle. We’ll look at three examples: one for one triangle, one for two triangles and one for no triangles.

**What are the possible outcomes of the ambiguous case?**

In this ambiguous case, three possible situations can occur: 1) no triangle with the given information exists, 2) one such triangle exists, or 3) two distinct triangles may be formed that satisfy the given conditions.

### In which of the following cases can we use the Law of Sines to solve a triangle?

The Law of Sines can be used to solve for the missing lengths or angle measurements in an oblique triangle as long as two of the angles and one of the sides are known.

### Why is there no ambiguous case for cosine law?

Originally Answered: Why are there only ambiguous cases in triangles for sine law and not cosine law? Because all angles of a triangle are between 0 and 180 degrees, there is only one angle with a given cosine and two angles with a given sine.

**How do you use the Law of Sines to solve for all possible triangles that satisfy the given conditions?**

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions….We will follow a process using 3 steps:

- use The Law of Sines first to calculate one of the other two angles;
- use the three angles add to 180° to find the other angle;
- use The Law of Sines again to find the unknown side.