In triangle ABC, angle C is 90 degrees BC = 4, sin (B) = 2√6 / 5 find AB

Given:

ABC – right-angled triangle;

Angle C = 90 degrees;

BC = 4;

sin (B) = 2√6 / 5;

Find AB.

Solution:

1 First, find cos a.

sin a = √ (1 – cos ^ 2 a) = √ (1 – (2√6 / 5) ^ 2) = √ (1 – 4 * 6/25) = √ (1 – 24/25) = √ ( 25/25 – 24/25) = √ (1/25) = 1/5;

Hence, sin a = 1/5.

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

sin A = BC / AB.

Hence, AB = BC / sin a;

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

AB = 4 / (1/5) = 4 * 5/1 = 4 * 5 = 20.

Answer: AB = 20.