In a right-angled triangle ABC with a right angle C, the length of the leg is CB = √ 13/4

univerkov | May 3, 2021 | education

In a right-angled triangle ABC with a right angle C, the length of the leg is CB = √ 13/4 and cos A = 6/7. Find the length of the other leg.

Since CosBAC = 6/7, then let AC = 6 * X cm, then AB = 7 * X cm.

Then, by the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2.

49 * X ^ 2 = 36 * X ^ 2 + 13/16.

13 * X ^ 2 = 13/16.

X ^ 2 = 1/16.

X = 1/4.

Then AC = 6 * 1/4 = 3/2 = 1.5 cm.

Answer: The length of the AC leg is 1.5 cm.

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