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.
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