The height BD of the rectangle of the triangle is 24 cm and cuts off the segment DC equal to 18 cm
| July 26, 2021 | education
The height BD of the rectangle of the triangle is 24 cm and cuts off the segment DC equal to 18 cm from the hypotenuse AC. Find AB and cos of angle A.
In a right-angled triangle ABC, the height BD is drawn from the vertex of the right angle to the hypotenuse, then BD ^ 2 = CD * AD.
AD = BD ^ 2 / CD = 576/18 = 32 cm.
In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = BD ^ 2 + AD ^ 2 = 576 + 1024 = 1600.
AB = 40 cm.
Then CosA = AD / AB = 32/40 = 0.8.
Answer: The length of the AB side is 40 cm, CosA = 0.8.
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