In an acute-angled triangle ABC, the heights AA1 and BB1 intersect at point O.

In an acute-angled triangle ABC, the heights AA1 and BB1 intersect at point O. Find the angle OCA if the angle BAC = 58 °.

Let us extend the OС segment to the intersection with the side AB and mark the point C1.

Segment CC1 passes through point O, the point of intersection of heights, then CC1 is the same height of triangle ABC, and then triangle ACC1 is rectangular.

Then the angle ACC1 = OCA = (180 – 90 – 58) = 32.

Answer: The OCA angle is 32.

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