In a right-angled triangle ABC, the angle is C = 90 degrees, AC = 4 cm, CB = 4√3 cm
| May 10, 2021 | education
In a right-angled triangle ABC, the angle is C = 90 degrees, AC = 4 cm, CB = 4√3 cm, CM is the median. Find the angle of the BCM.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AB ^ 2 + BC ^ 2 = 16 + 48 = 64.
AB = 8 cm.
According to the property of the median, drawn from the vertex of the right angle to the hypotenuse, the length of the median is equal to half the length of the hypotenuse.
CM = BM = AM = AB / 2 = 8/2 = 4 cm.
In triangle CAM, the lengths of all sides are equal, AC = AM = CM = 4 cm, then triangle CAM is equilateral, and all its internal angles are 60.
Then the angle ВСМ = АСВ – АСМ = 90 – 60 = 30.
Answer: The BCM angle is 30.
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