In triangle ABC, angle ABC = 90 °, BD parallel to AC, AD = 12 cm. CD = 16 cm. Find AB, BC, BD , cos A, tg C.
| May 29, 2021 | education
Since BD the height of triangle ABC is drawn to the hypotenuse, then BD ^ 2 = AD * CD = 12 * 16 = 192.
ВD = 8 * √3 cm.
In a right-angled triangle ABD, according to the Pythagorean theorem, AB ^ 2 = BD ^ 2 + AD ^ 2 = 192 + 144 = 336.
AB = 4 * √21 cm.
In a right-angled triangle BCD, according to the Pythagorean theorem, BC ^ 2 = BD ^ 2 + CD ^ 2 = 192 + 256 = 448.
BC = 8 * √7 cm.
AC = AD + CD = 12 + 16 = 28 cm.
CosBAC = AB / AC = 4 * √21 / 28 = √21 / 7.
tgACB = AB / BC = 4 * √21 / 8 * √7 = √3 * √7 / 2 * √7 = √3 / 2.
Answer: AB = 4 * √21 cm, BC = 8 * √7 cm, BD = 8 * √3 cm, CosBAC = √21 / 7, tgACB = √3 / 2.
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