In right-angled triangle ABC, angle C is 90 degrees, bisectors CD and BE meet at point O.
| September 8, 2021 | education
In right-angled triangle ABC, angle C is 90 degrees, bisectors CD and BE meet at point O. BOC is 95 degrees. Find the largest acute angle.
Since CD is the bisector of a right angle, the angle BCD = BCO = 90/2 = 45.
In the BОС triangle, the angle СBО = (180 – ВСО – ВОС) = (180 – 45 – 95) = 40.
The segment BE is the bisector of the angle ABC, then the angle ABC = 2 * CBO = 2 * 40 = 80.
Answer: The largest acute angle of the triangle is 80.
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