# Worksheet: The Ambiguous Sine Rule

Q1:

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 , , or , ,
• C , ,
• D , , or , ,

Q2:

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 , , or , ,
• C , ,
• 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 , , or , ,
• C , ,
• 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.