The heights of the triangle ABC intersect at point O, OC = AB. Find the angle at the vertex C.
| April 26, 2021 | education
Let BH and CE be the heights of the triangle ABC (H belongs to AC, E belongs to AB).
Consider triangles СOН and AВН: both triangles are rectangular, AB = OС (by condition).
Hence, BH = CH (as projections of equal hypotenuses).
In the СВН triangle: ВН = CH, it means the triangle is isosceles, the angle НВС = the angle НСВ = (180 ° – 90 °): 2 = 45 °.
Answer: angle C is 45 °
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