# In triangle ABC BM is the median and BH is the height. It is known that AC = 64, HC = 16, and ∠ACB = 37 °. Find the angle AMB.

May 31, 2020 | Education

| Since BM is the median, it means AM = MC = AC / 2 = 64/2 = 32

Consider the MBC triangle.

MH = MC-HC = 32-16 = 16, i.e. it turns out that MC = HC.

BH for this triangle is not only the height, but also the median. This is a property of an isosceles triangle.

By the property of an isosceles triangle: ∠BMC = ∠ACB = 37 °.

∠AMB = 180 ° -∠BMC = 180 ° -37 ° = 143 ° (as it is adjacent)

Answer: 143

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.