In triangle ABC, angle C is obtuse, BC = 15 cm, AB = 20 cm, BK is the height of the triangle, BK = 12 cm.

In triangle ABC, angle C is obtuse, BC = 15 cm, AB = 20 cm, BK is the height of the triangle, BK = 12 cm. Find the length of the AC side.

VK is the height that does not lie in the triangle ABC. The AВK triangle is rectangular. By the Pythagorean theorem, we calculate AK: AK ^ 2 = AB ^ 2 -ВK ^ 2. AK ^ 2 = 400 – 144. AK ^ 2 = 256. AK = 16.
The CBC triangle is rectangular. By the Pythagorean theorem, we find the CK:
CK ^ 2 = CB ^ 2 – BK ^ 2.
CK ^ 2 = 225 – 144 = 81.
CK = 9.
AC = AK – CK.
AC = 16 – 9 = 7.
Answer: 7 cm.