Given ABC a right-angled triangle, height CD = 12 cm A = 16 cm, find the sides AC BC AB BD.

In this right-angled triangle ABC, the height CD, drawn from angle C, is the leg of the newly formed right-angled triangle ACD, where both legs are known according to the condition of the task;

To find the hypotenuse of AC, we apply the Pythagorean theorem;

AC ^ 2 = AD ^ 2 + CD ^ 2 = 16 ^ 2 + 12 ^ 2 = 40, that is, AC = 20 cm;

Consider triangles ACB and CDB, in which the side CB is common;

Triangle CDB: we denote the leg DB by “x”, then the hypotenuse CB = √ (CD ^ 2 + DB ^ 2);

CB = √ (144 + x ^ 2);

From the triangle ACB we express the side CB = √ (16 + x) ^ 2 – 20 ^ 2, hence we have:

144 + x ^ 2 = 256 + 32 x + x ^ 2 – 400; x = √9 = 3;

Means: CB = √144 + 9 = √153 cm; DB = 3 cm; AB = 16 + 3 = 19 cm; AC = 20 cm.