In a right-angled triangle ABC Angle A = 90 degrees, AB = 20cm, Height AD = 12cm. Find AC and cos of angle C.

1. Using the Pythagorean tower, we calculate the length of the segment BD:

BD ^ 2 = AB ^ 2 – AD ^ 2 = 20 ^ 2 -12 ^ 2 = 400 – 144 = 256;

ВD = √256 = 16 cm.

2. The height АD, drawn to the hypotenuse, is equal to √ВD x DC;

AD ^ 2 = BD x DC;

DC = AD ^ 2: BD = 144: 16 = 9 cm.

3. Calculate the length of the aircraft:

16 + 9 = 25 cm.

4. Using the Pythagorean tower, we calculate the length of the AS:

AC = √BC ^ 2 – AB ^ 2 = √25 ^ 2 – 20 ^ 2 = √625 – 400 = √225 = 15 cm.

5. The cosine of angle C is equal to the ratio AC / BC = 15/25 = 0.6.

Answer: the cosine of the angle C is 0.6, the length of the AC is 15 cm.