In the given figure, ∠ AMN = ∠ MBC = 76°. If a, b and c are the lengths of AM, MB and BC respectively then express the length of MN in terms of a, b and c.

Question

Philoid · Accepted Answer

In ΔAMN and ΔABC

∠AMN = ∠ABC = 76° (Given)

∠A = ∠A (common)

By AA Similarity criterion, ΔAMN ~ Δ ABC

If two triangles are similar, then the ratio or the their corresponding sides are proportional

In the given figure, ∠AMN = ∠MBC = 76°. If a, b and c are the lengths of AM, MB and BC respectively then express the length of MN in terms of a, b and c.