Find the sine, cosine and tangent of angles A and B of triangle ABC with right angle C if BC = 1 dm, AC = 3 dm

By the Pythagorean theorem, we find the hypotenuse AB:
AB = √ (AC² + BC²) = √ (9 + 1) = √10 (dm).
Let’s use the definition of sine, cosine and tangent of an angle and find them for the angles A and B of this triangle.
Angle A.
Sin A = BC / AB = 1 / √10.
Cos A = AC / AB = 3 / √10.
Tg A = BC / AC = 1/3.
Angle B.
Sin B = AC / AB = 3 / √10.
Cos B = BC / AB = 1 / √10.
Tg B = AC / BC = 3/1 = 3.
Answer: sine, cosine, tangent of angles A and B are respectively equal: 1 / √10, 3 / √10, 1/3 and 3 / √10, 1 / √10, 3.