# Lesson Worksheet: Ambiguous Case of the Law of Sines Mathematics

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

**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.

**Q10: **

Given an isosceles triangle with sides , the side , and the , find the length of the side approximate to the nearest one decimal place.

**Q12: **

In a triangle , , , and . How many triangles can be formed?

- ATwo triangles
- BOne triangle
- CZero triangles
- DThree triangles
- EAn infinite number of triangles

**Q13: **

For a triangle , , , and . How many triangles can be formed?

- AAn infinite number of triangles
- BTwo triangles
- CThree triangles
- DOne triangle
- EZero triangles

**Q14: **

In a triangle , , , and . How many triangles can be formed?

- AAn infinite number of triangles
- BThree triangles
- CTwo triangles
- DOne triangle
- EZero triangles

**Q15: **

In a triangle , , , and . How many triangles can be formed?

- AThree triangles
- BOne triangle
- CAn infinite number of triangles
- DTwo triangles
- EZero triangles

**Q16: **

In the given figure, if is an acute angle and , how many triangles can be formed?

- ATwo triangles
- BOne triangle
- CThree triangles
- DZero triangles
- EAn infinite number of triangles

**Q17: **

In the given figure, if is an obtuse angle and , how many triangles can be formed?

- AAn infinite number of triangles
- BTwo triangles
- COne triangle
- DZero triangles
- EThree triangles

**Q18: **

For a triangle , , , and . How many triangles can be formed?

- AThree triangles
- BNo triangles can be formed
- CTwo triangles
- DOne triangle
- EAn infinite number of triangles

**Q19: **

For a triangle , , , and . How many possible solutions are there for each of the other lengths and angles?

- AOne solution
- BZero solutions
- CTwo solutions
- DThree solutions
- EAn infinite number of solutions

**Q20: **

For a triangle , , , and . How many triangles can be formed?

- AAn infinite number of triangles
- BThree triangles
- COne triangle
- DTwo triangles
- ENo triangles can be formed

**Q21: **

For a triangle , , , and . Find all the possible measures of to the nearest degree.

**Q22: **

For a triangle , , , and . Find all the possible measures of to the nearest degree.

- A and
- B
- C and
- D and
- E

**Q23: **

For a triangle , , , and . How many possible solutions are there for each of the other lengths and angles?

- AOne solution
- BAn infinite number of solutions
- CThree solutions
- DTwo solutions
- EZero solution

**Q24: **

is a triangle in which , , and . If the triangle exists, find all the possible values of angle to the nearest second.

- AThe triangle does not exist.
- B
- C or
- D or
- E

**Q25: **

For the triangle , , , and . Find all the possible measures of to the nearest degree.