Sides AB and A'B' are parallel. 1. Are triangles ABC and A'B'C similar? Explain how you know. 2. Find the length of segment AB or explain why you cannot find it.

Question

Answer 1

This triangle similar, because angle C is common and angle B = B' by property of parallel lines.

By sine law sin40°/6 = sinA/9; sinA = 3sin40°/2 = 0.9642; A = sin^-10.9642 = 74.62° or A = 180° - 74.62 = 105.38°.

So C = 180° - (40°+ 74.62°) = 65.38° or C = 180° - (40° + 105.38°) = 34.62°.

Then, by cosine law you can find AB from Δ ABC (2 values with angle B = 65.38° and B = 34.62°.

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