In triangle ABC, angle C is 90, AB = 5 roots of 2, AC = 5. Find tgA

Triangle ABC is rectangular, since its angle C is right.

The tangent of an acute angle of a right-angled triangle is the ratio of the opposite leg to the adjacent leg.

tg À = BC / AC.

We know the hypotenuse AB = 5√2 and the adjacent leg AC = 5. Find the opposite leg BC according to the Pythagorean theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

AB² = AC² + BC²;

BC² = AB² – AC²;

ВС² = (5√2) ² – 5² = (25 * 2) – 25 = 50 – 25 = 25;

BC = √25 = 5.

tg A = 5/5 = 1.

Answer. tg A = 1.