In a right-angled triangle, the AC leg is 3 cm, the hypotenuse is 6 cm, find the acute angle opposite the AC leg.

Given:

ABC – right triangle;

Angle C = 90 degrees;

Leg AC = 3;

Hypotenuse AB = 6;

Let us find an acute angle opposite the leg AC, that is, angle B.

Decision:

Let us find the BC by the Pythagorean theorem.

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

6 ^ 2 = 3 ^ 2 + BC ^ 2;

36 = 9 + BC ^ 2;

BC ^ 2 = 36 – 9;

BC ^ 2 = 27;

BC = 3 √3;

2) sin b = AC / AB = 3/6 = ½;

sin b = ½;

b = pi / 6;

This means that the acute angle of the AC opposite the leg is 30 degrees.

Answer: 30 degrees.