In a right-angled triangle, the angle between the height and the median drawn

In a right-angled triangle, the angle between the height and the median drawn from the apex of the obtuse angle is 3 degrees. Find the larger angle of the triangle.

In a right-angled triangle CHM, the angle CHN = (90 – MSN) = (90 – 3) = 87.

The BMC angle is adjacent to the CMH angle, the sum of which is 180, then the BMC angle = (180 – CMH) = (180 – 87) = 93.

Since CM is the median of the triangle ABC, then CM = BM, and then the triangle BCM is isosceles, and then the angle MBC = MCB = (180 – 93) / 2 = 43.5.

Angle BАС = 90 – СBА = 90 – 43.5 = 46.5.

Angle BАС> АBС.

Answer: The larger angle of the triangle is 46.5.

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