In a right-angled triangle ABC, the length of the hypotenuse AB wound 11 is the root of 2 COSA = 7/11 Calculate BC.

Since we know the cosine of angle A, we calculate the value of the sine of angle A using the basic trigonometric formula sin²a + cos²a = 1:

cosA = 7/11;

sinA = √ (1 – cos²A) = √ (1 – (7/11) ²) = √ (1 – 49/121) = √ (121/121 – 49/121) = √ (72/121) = √72 / √121 = √ (36 * 2) / 11 = 6√2 / 11.

Let us express the sine of angle A (sine is the ratio of the opposite leg to the hypotenuse):

sinA = BC / AB.

Substitute the known data and calculate the BC value.

sinA = 6√2 / 11, AB = 11√2.

6√2 / 11 = BC / 11√2.

BC = 6√2 * 11√2 / 11 = 6 * 2 = 12.

Answer: BC length is 12.