The median BM is drawn in an isosceles triangle ABC with base AC. angle ABM = 60 degrees. BM = 6cm. Find the angles of triangle ABC and its side
1. According to the properties of an isosceles triangle, the BM median is the height and
bisector. That is, the angle AMB = 90 °. Angle ABC = 60 ° x 2 = 120 °.
2. We calculate the degree measure of the angle BAM:
Angle BAM = 180 ° – 90 ° – 60 ° = 30 °. angle BAM = angle ACB = 30 °.
3. In the AVM triangle, the perpendicular BM is the leg opposite the 30 ° angle.
Therefore, its length is half the length of the hypotenuse AB.
AB = 6 x 2 = 12 cm.
Answer: angle ABC = 120 °, angle BAC = angle ACB = 30 °, the length of the side of the triangle is 12 cm.
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