The height BD of a right-angled triangle ABC is 24 cm and cuts off the segment DC = 18 cm
| April 6, 2021 | education
The height BD of a right-angled triangle ABC is 24 cm and cuts off the segment DC = 18 cm from the hypotenuse AC. Find AB and cosine A.
Since the height BD of the right-angled triangle ABC is drawn from the vertex of the right angle, the square of the length of the height is equal to the product of the lengths of the segments by which the height divides the hyptenuse.
BD ^ 2 = AD * CD.
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 = AD ^ 2 + BD ^ 2 = 1024 + 576 = 1600.
AB = 40 cm.
Determine the cosine of the angle BAC.
CosBAC = AD / AB = 32/40 = 0.8.
Answer: The length of side AB is 40 cm, the cosine of angle A is 0.8.
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