# In a right-angled triangle, the hypotenuse is 10 cm, one of the legs is half the size of the other.

July 29, 2021 | education

| **In a right-angled triangle, the hypotenuse is 10 cm, one of the legs is half the size of the other. Find the corners of a right triangle.**

Let the length BC = X cm, then AB = 2 * X cm.

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

100 = 4 * X ^ 2 + X ^ 2 = 5 * X ^ 2.

X ^ 2 = 100/5 = 20.

X = BC = √20 = 2 * √5 cm.

Then CosC = BC / AC = 2 * √5 / 10 = 0.45.

Angle ACB = arcos0.447 = 63.40.

Then the angle BAC = 90 – 63.4 = 26.60.

Answer: The acute angles are 63.40 and 26.60.

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