Based on the diagram, which expresses all possible lengths of segment AB? AB = 25 27 < AB < 81 AB = 85 AB 81

Question

Mathematics

Cora Bishop

28 November, 09:03

Based on the diagram, which expresses all possible lengths of segment AB? AB = 25 27 < AB < 81 AB = 85 AB 81

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Alexandra · Answer 1

The answer

according to the figure, we can solve this problem only by applying sines rule:

that is

sinA/a = sinB/b = sinC / c

As we observe, sin A / 54 = sin B/27 = sin C / c, and c = AB

besides, sinC > sinB > sinA, so the only answer possible is

27 < AB < 81