The legs of a right-angled triangle are 5 cm and 12 cm, find the cosine of the angle adjacent to the smaller leg.

The cosine of an angle in a right-angled triangle is the ratio of the adjacent leg to the hypotenuse. Since the AC side is the smaller leg, the angle adjacent to it is the angle ∠A.

Thus:

cos A = AC / AB.

To do this, we calculate the length of the hypotenuse AB. Let’s apply the Pythagorean theorem:

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

AB ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169;

AB = √169 = 13 cm.

cos A = 5/13 ≈ 0.385.

Answer: The cosine of the angle adjacent to the smaller leg is 0.385.