In a right-angled triangle ABC, angle C = 90, sin A = √15 / 4, BC = √5. Find AB.

Find AB in a right-angled triangle ABC.

It is known that the angle C = 90 °;

sin A = √15 / 4;

BC = √5.

Decision:

sin a = BC / AB, AB – hypotenuse, BC – leg.

Substitute the known values and calculate the value of the hypotenuse AB.

√15 / 4 = √5 / AB;

√5 * √3 / 4 = √5 / AB;

1 * √3 / 4 = 1 / AB;

AB = 4 * 1 / √3;

AB = 4 / √3;

As a result, we got that the hypotenuse AB of triangle ABC is equal to 4 / √3.

Answer: AB = 4 / √3.