# Worksheet: Ambiguous Case of the Law of Sines

In this worksheet, we will practice using the rule of sines to solve SSA (side-side-angle) ambiguous triangles.

**Q2: **

is a triangle where , and . Find all possible values for the other lengths and angles giving lengths to two decimal places and angles to the nearest second.

- A , , or , ,
- B , , or , ,
- C , , or , ,
- D , , or , ,

**Q3: **

is a triangle, where , , and . If the triangle exists, find all the possible values for the other lengths and angles giving the lengths to two decimal places and angles to the nearest second.

- A , ,
- B , ,
- C , , or , ,
- D , , or , ,

**Q4: **

is a triangle, where , , and . If the triangle exists, find all the possible values for the other lengths and angles in , giving the lengths to two decimal places and angles to the nearest degree.

- A cm, , and
- B cm, , and
- CThe triangle does not exist.

**Q5: **

For the given figure, , , and . Use the law of sines to work out the measure of . Give your answer to two decimal places.

**Q6: **

is a triangle, where , , and . If the triangle exists, find all the possible values for the other lengths and angles in giving the lengths to two decimal places and angles to the nearest degree.

- A , ,
- BThe triangle does not exist.
- C , ,

**Q7: **

is a triangle where , and . If the triangle exists, find all the possible values for the other lengths and angles in giving lengths to two decimal places and angles to the nearest second.

- A , ,
- B , , or , ,
- C , ,
- D , ,
- ENo triangle exists.

**Q8: **

is a triangle, where , , and . Find the missing length rounded to three decimal places and the missing angles rounded to the nearest degree.

- A , ,
- B , ,
- C , ,
- D , ,