# 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.

Q1:

is a triangle, where , cm, and cm. How many possible solutions are there for the other lengths and angles?

• Ano solutions
• Bone solution
• Ctwo solutions

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, ,

Q9:

is a triangle, where , cm, and cm. How many possible solutions are there for the other lengths and angles?

• Aone solution
• Bno solutions
• Ctwo solutions

Q10:

is a triangle, where , cm, and cm. How many possible solutions are there for the other lengths and angles?

• Ano solutions
• Bone solution
• Ctwo solutions