In a right-angled triangle ABC, legs AC = 6 and BC = 8 are known.
| July 17, 2021 | education
In a right-angled triangle ABC, legs AC = 6 and BC = 8 are known. Point D is chosen on hypotenuse AB so that AD = 7.2. Find the length of the CD segment.
By the Pythagorean theorem we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 64 + 36 = 100.
AB = 10 cm.
Determine the cosine of the angle BAC
CosBAC = AC / AB = 8/10 = 0.8.
In the triangle ACD, using the cosine theorem, we determine the length of the side CD.
CD ^ 2 = AC ^ 2 + AD ^ 2 – 2 * AC * AD * CosCAB = 64 + 51.84 – 2 * 8 * 7.2 * 0.8 = 115.84 – 92.16 = 23.68 = 64 * 0.37.
СD = 8 * √0.37 cm.
Answer: The length of the CD segment is 8 * √0.37 cm.
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