In a triangle, the angle C is straight, BC = 5cm, AC = 12, ∠A = α. Find sinα, cosα, tgα.

In the problem, the leg AC = 12 cm adjacent to the corner A and the opposite leg BC = 5 cm are given.

Let us find the hypotenuse AB by the Pythagorean theorem:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AB ^ 2 = 5 ^ 2 + 12 ^ 2;

AB ^ 2 = 25 ^ 2 + 144 ^ 2;

AB ^ 2 = 169;

AB = √169;

AB = 13 cm.

The sine of angle A is equal to the ratio of the opposite leg BC to the hypotenuse AB:

Sin A = 5: 13 = 5/13.

The cosine of angle A is equal to the ratio of the adjacent leg AC to the hypotenuse AB:

Cos A = 12: 13 = 12/13.

The tangent of angle A is equal to the ratio of the opposite leg BC to the adjacent AC:

Tg A = 5: 12 = 5/12.