In triangle ABC AB = BC, AB = 4, CH height is √7. Find cosABC.

1. We calculate the length of the leg BN of the right-angled triangle BCH, using the formula
Pythagorean theorems:
BH ^ 2 = BC ^ 2 – CH ^ 2.
VN = √BC ^ 2 – CH ^ 2 = √4 ^ 2 – (√7) ^ 2 = √16 – 7 = √9 = 3 units.
2. The BN leg is the side of the ABC angle, that is, adjacent to it. BC – hypotenuse.
3. The cosine of the angle ABC = BN / BC = 3: 4 = 0.75.
Answer: the cosine of the angle ABC = 0.75.