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.

Q1:

How many triangles can be formed for a triangle 𝐴𝐵𝐶 with 𝑏=5cm, 𝑎=2cm, and 𝑚𝐴=155?

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

Q2:

𝐴𝐵𝐶 is a triangle, where 𝑚𝐵=110, 𝑏=16 cm, and 𝑐=12 cm. How many possible solutions are there for the other lengths and angles?

  • Ano solutions
  • Bone solution
  • Ctwo solutions

Q3:

For a triangle 𝐴𝐵𝐶, 𝑎=6cm, 𝑏=5cm, and 𝑚𝐴=40. How many triangles can be formed?

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

Q4:

For a triangle 𝐴𝐵𝐶, 𝑎=2cm, 𝑏=5cm, and 𝑚𝐴=35. How many triangles can be formed?

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

Q5:

For a triangle 𝐴𝐵𝐶, 𝑎=5cm, 𝑏=9cm, and 𝑚𝐴=25. How many triangles can be formed?

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

Q6:

For a triangle 𝐴𝐵𝐶, 𝑎=2cm, 𝑏=5cm, and 𝑚𝐵=40. Find all the possible measures of 𝐴 to the nearest degree.

Q7:

For a triangle 𝐴𝐵𝐶, 𝑎=3cm, 𝑏=9cm, and 𝑚𝐴=10. Find all the possible measures of 𝐵 to the nearest degree.

  • A149 and 25
  • B31
  • C31 and 149
  • D31 and 25
  • E25

Q8:

𝐴𝐵𝐶 is a triangle in which 𝑎=5cm, 𝑏=8cm, and 𝑚𝐴=36. If the triangle exists, find all the possible values of angle 𝐵 to the nearest second.

  • AThe triangle does not exist.
  • B𝑚𝐵=70742
  • C𝑚𝐵=70742 or 𝑚𝐵=1095118
  • D𝑚𝐵=70718 or 𝑚𝐵=1095142
  • E𝑚𝐵=1095118

Q9:

𝐴𝐵𝐶 is a triangle, where 𝐵𝐶=13.8 cm, 𝐴𝐶=21.2 cm, and 𝑚𝐴=21. Find all possible values of length 𝐴𝐵 giving the answer to three decimal places.

  • A𝐴𝐵=22.651cm or 𝐴𝐵=2.859cm
  • B𝐴𝐵=62.625cm or 𝐴𝐵=16.543cm
  • C𝐴𝐵=31.312cm or 𝐴𝐵=8.272cm
  • D𝐴𝐵=15.656cm or 𝐴𝐵=4.136cm

Q10:

𝐴𝐵𝐶 is a triangle where 𝑏=28cm, 𝑐=17cm and 𝑚𝐶=32. Find all the possible values for the perimeter giving the answer to two decimal places.

  • A77.04 cm, 45 cm
  • B77.04 cm, 60.45 cm
  • C49.04 cm, 60.45 cm
  • D68.75 cm, 53.3 cm

This lesson includes 26 additional questions and 247 additional question variations for subscribers.

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