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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, 𝐴 𝐡 = 1 1 , 𝐡 𝐢 = 9 , and π‘š ∠ 𝐡 𝐴 𝐢 = 4 1 ∘ . Use the law of sines to work out the measure of ∠ 𝐴 𝐢 𝐡 . Give your answer to two decimal places.