The height BD of a right-angled triangle is 24 cm and cuts off a segment DC equal to 18 cm
| September 6, 2021 | education
The height BD of a right-angled triangle is 24 cm and cuts off a segment DC equal to 18 cm from the hypotenuse AC. find AB and cosA
Since triangle ABC is rectangular, and its height BD is drawn from the vertex of a right angle, then the square of its length is equal to the product of the segments into which BD divides AC.
BD ^ 2 = AD * CD.
AD = BD ^ 2 / CD = 576/18 = 32 cm.
From the right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg AB.
AB ^ 2 = AD ^ 2 + BD ^ 2 = 1024 + 576 = 1600.
AB = 40 cm.
CosBAD = AD / AB = 32/40 = 4/5.
Angle BAD = arcos (4/5).
Answer: The length of the side AB is 40 cm, the angle BAD is equal to arcos (4/5).
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