Find the area of the triangle ABC, angle A = 90º, BC = 20 cm, AB = 16 cm.

We know that the angle A = 90º, therefore, the triangle ABC is rectangular, then BC is the hypotenuse, and AB is the leg. By the Pythagorean theorem, we can find the leg AC:
BC ^ 2 = AC ^ 2 + AB ^ 2
then
AC ^ 2 = BC ^ 2- AB ^ 2
AC ^ 2 = 20 ^ 2-16 ^ 2
AC ^ 2 = 400-256
AC ^ 2 = 144
AC = √144
AC = 12 (cm)
The area of a right-angled triangle is half the product of the legs
S = 1/2 * AB * AC
S = 1/2 * 16 * 12 = 96 (cm ^ 2)
Answer: S = 96 cm ^ 2