In triangle ABC, angle C is 90∘, sinA = 11/14, AC = 10√3. Find AB.

Given:

ABC – right triangle;

Angle C = 90 degrees;

AC = 10√3;

sin A = 11/14;

Find AB.

Decision:

sin a = √ (1 – cos ^ 2 a) = √ (1 – (11/14) ^ 2) = √ (1 – 121/196) = (196/196 – 121/196) = √ ((196 – 121) / 196) = √75 / 14 = √25 * √5 / 14 = 5/14 * √5;

In order to find the hypotenuse AB of the triangle ABC, we use the formula:

cos A = AC / AB.

Hence, AB = AC / cos a;

Substitute the known values into the formula and find the hypotenuse AB.

AB = 10√3 / (5 * √5 / 14) = 10 * √3 * 14 / (5 * √5) = 2 * 14 * √15 = 28 * √15 = 28√15;

Answer: AB = 28√15.