In the ABC triangle, AC = BC, the CH height is 26, cosA = √2 / 2. Find AB.
| February 24, 2021 | education
Since, by condition, CosBAC = √2 / 2, then the angle BAC = arcos (√2 / 2) = 45.
By condition, AC = BC, then the triangle ABC is isosceles, which means the angle ABC = BAC = 45.
Then the angle ACB = 180 – 90 – 90 = 90, and the triangle ABC is rectangular.
CH – the height of the triangle ABC, then the triangles AСН and СВН are rectangular and isosceles.
AH = CH = BH = 26 cm.
AB = AH + BH = 26 + 26 = 52 cm.
Answer: The length of the AB side is 52 cm.
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