In a right-angled triangle ABC with a right angle C, the hypotenuse AB = 20 cm

In a right-angled triangle ABC with a right angle C, the hypotenuse AB = 20 cm and the leg BC = 12 cm. Find the height CH of this triangle.

1. We calculate the length of the AC leg using the formula of the Pythagorean theorem:

AC ^ 2 = AB ^ 2 – BC ^ 2.

AC = √AB ^ 2 – BC ^ 2 = √20 ^ 2 – 12 ^ 2 = √400 – 144 = √256 = 16 cm.

2. Calculate the area of the triangle ABC:

the area of the triangle ABC = BC x AC / 2 = 12 x 16: 2 = 192: 2 = 96 cm ^ 2.

3. Calculate the length of the CH height using another formula for calculating the area of a triangle,

through the hypotenuse AB and the height of the CH:

the area of the triangle ABC = AB x CH / 2.

96 = AB x CH / 2.

CH = 96 x 2: 20 = 192: 20 = 9.6 cm.

Answer: CH = 9.6 cm.