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How many triangles ABC can have ∠A = 40°, AB = 6 cm and BC = 4.5 cm?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • ATwo
  • BInfinitely many
  • CNone
  • DExactly one

Step-by-Step Solution

This is SSA. The distance from B to the other arm is 6 sin 40° ≈ 3.86 cm, which is less than 4.5 cm (and 4.5 < 6), so the 4.5 cm side can meet that arm at two points. Two different triangles fit — which is why SSA is not a rule.
Answer: A) Two

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