In triangle ABC, angle C = 90 degrees, cosine A = 0.8, BC = 3. Find AB.

Given:

ABC – right triangle;

Angle C = 90 degrees;

BC = 5;

cos A = 0.8;

Find AB.

Decision:

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

cos A = AC / AB or sin a = BC / AB, AC – unknown.

Find sin a = √ (1 – cos ^ 2 a) = √ (1 – 0.8 ^ 2) = √ (1 – 0.64) = √0.36 = 0.6;

Hence, AB = BC / sin a;

Substitute the known values sin a = 0.6 and BC = 5 into the formula and find the hypotenuse AB.

AB = 5 / 0.6 = 5 / (6/10) = 5 / (3/5) = 5/1 * 5/3 = 5 * 5/3 = 25/3 = 24/3 + 1/3 = 8 1 / 3;

Answer: AB = 8 1/3.