In triangle ABC, angle C = 90 degrees, sine A = 3/4, AC = 6√7. Find AB

In triangle ABC:

Angle C = 90 °;
sin A = 3/4;
AC = 6√7.
Find AB.

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

cos A = AC / AB.

Hence, AB = AC / cos a, where cos a = √ (1 – sin ^ 2 a).

cos a = √ (1 – (3/4) ^ 2) = √ (1 – 9/16) = √ (16/16 – 9/16) = √5 / √16 = √5 / 4;

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

AB = 6√7 / (√5 / 4) = 6√7 * 4 / √5 = 24 * √7 / √5 = 24√ (7/5);

Answer: AB = 24√ (7/5).