In triangle ABC, angle c is 90 degrees BC = 5, tg A = 1 / 2√2 find AB.

Given:

ABC – right triangle;

Angle C = 90 degrees;

BC = 5;

tg A = √2 / 2;

Find AB.

Decision:

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

tg A = BC / AB;

Hence, AB = BC / tg a;

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

AB = 5 / (√2 / 2) = 5 * 2 / √2 = 10 / √2 = 10 * √2 / (√2 * √2) = 10 * √2 / 2 = 10/2 * √2 = 5 * √2;

Answer: AB = 5√2.