In a right-angled triangle ABC leg AC = 20 and the height CH, lowered to the hypotenuse, is 3√39.

In a right-angled triangle ABC leg AC = 20 and the height CH, lowered to the hypotenuse, is 3√39. Find the cos of the angle CAB.

1) we use the Pythagorean theorem to find the segment AN

c ^ 2 = a ^ 2 + b ^ 2, AC ^ 2 = CH ^ 2 + AH ^ 2, AH ^ 2 = AC ^ 2 – CH ^ 2

substitute the values of the segments from the condition

AH ^ 2 = (20) ^ 2 – (3 roots of 39) ^ 2 = 400 – 9 * 39 = 400 – 351 = 49

AH = √49 = 7

2) By the cosine theorem, we find the value of the angle CAB

cosCAB = AH: CA = 7: 20 = 0.35