Find the angle A of triangle ABC if its median BM is half of the side AC

| February 6, 2021 | education

Find the angle A of triangle ABC if its median BM is half of the side AC, and the angle BTC formed by the bisector BT and side AC is 65 degrees.

Since, by condition, the median BM is equal to half the length of the AC side of the triangle, AM = BM = CM. and therefore the vertices of the triangle ABM lie on a circle centered at the point M, and the AC side is the diameter of this circle.

The inscribed angle ABC rests on the arc AC, the degree measure of which is 360/2 = 180, then the angle ABC = 90, and the triangle ABC is rectangular.

Since BT is the bisector of the right angle, the angle CBT = 90/2 = 45.

Then, in the ВСT triangle, the ВСT angle = (180 – 45 – 65) = 70.

The sum of the acute angles of a right-angled triangle is 90, then the angle BAC = 90 – 70 = 20.

Answer: Angle A is 20.



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