In triangle ABC, angle C is 90 degrees, BC = 4.8, cosA = 7/25. Find AB.

Given:

ABC – right triangle;

Angle C = 90 °;

BC = 4.8;

cos A = 4/25;

Find AB.

Solution:

1) sin a = √ (1 – cos ^ 2 a) = √ (1 – (4/25) ^ 2) = √ (1 – 16/625) = √609 / 25;

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 = 4.8 / (√609 / 25) = 4.8 * 25 / √609 = 120 / √609;

Answer: AB = 120 / √609.