In triangle ABC the heights AE and CD are drawn. It is known that BD = 18, BC = 30, AE = 20. Find the side AB.
| July 23, 2021 | education
From the right-angled triangle ВСD, according to the Pythagorean theorem, we define the leg СD.
CD ^ 2 = BC ^ 2 – BD ^ 2 = 900 – 324 = 576.
СD = 24 cm.
From triangle ВСD Sin СВD = СD / ВС = 24/30 = 4/5.
From triangle ABE SinABE = AE / AB = 20 / AB.
Angle CBD = ABE, then SinCBD = SinABE.
4/5 = 20 / AB.
AB = 20 * 5/4 = 25 cm.
Answer: The segment AB is 25 cm.
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