In a right-angled triangle ABC, leg AB = 3, leg BC = 4, Find the sine, cosine, tangent, and cotangent of angle A.

ABC: angle B = 90 degrees, AB = 3 and BC = 4 – legs.
Let us find the length of the hypotenuse AC by the Pythagorean theorem:
AC = √ (AB ^ 2 + BC ^ 2);
AC = √ (3 ^ 2 + 4 ^ 2) = √ (9 + 16) = √25 = 5.
1. The sine of an angle in a right-angled triangle is the ratio of the opposite leg angle to the hypotenuse. In the triangle ABC opposite the angle A lies the leg BC, therefore:
sinA = BC / AC = 4/5 = 0.8.
2. The cosine of an angle in a right-angled triangle is the ratio of the leg adjacent to the angle to the hypotenuse. In triangle ABC, leg AB is adjacent to angle A, therefore:
cosA = AB / AC = 3/5 = 0.6.
3. The tangent of an angle in a right-angled triangle is the ratio of the opposite leg to the adjacent leg:
tgA = BC / AB = 4/3 = 1, [3].
4. The cotangent of an angle in a right-angled triangle is the ratio of the leg adjacent to the angle to the opposite leg:
ctgA = AB / BC = 3/4 = 0.75.
Answer: sinA = 0.8; cosA = 0.6; tgA = 1, [3]; ctgA = 0.75.