For a right-angled triangle BCD ∠С = 90 °, BM is the bisector of the triangle, ∠CBD = 60 °. Find the length of the CD leg if CM = 8cm.
The problem presented in the original task provides for the skills of using general terms and definitions of mathematical science, which contribute to the determination of various sizes of the geometric figure represented by the triangle. Due to the fact that, according to the initial task, one of the angles of the triangle is 90 °, the desired triangle is rectangular. With that said:
1) BM = 2CM = 16, because BM – bisector;
2) BC = √ (BM ^ 2 -CM ^ 2) = √ (16 ^ 2 – 8 ^ 2 = 8√3 cm;
3) ∠CBD = 60; ∠CDB = 30; BD = 2BC = 2 * 8√3 = 16√3;
4) CD = √ (BD ^ 2 – BC ^ 2 = 3 * 8 = 24 cm.
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