In a right-angled triangle abc (angle c = 90 degrees), the median cm is 6 cm

| February 4, 2021 | education

In a right-angled triangle abc (angle c = 90 degrees), the median cm is 6 cm, find the modules of vectors ab and ac if the angle a = 30 degrees

By the property of the median of a right-angled triangle, its length is equal to half the length of the hypotenuse AB. Then AB = 2 * CM = 2 * 6 = 12 cm.

Since the modulus of the vector is the length of the segment between the beginning and the end of the vector, then | AB | = AB = 12 cm.

The ACB triangle is isosceles, CM = AM = 6 cm, then the angle AMC = 180 – 30 – 30 = 1200.

By the cosine theorem, we define the length of the segment AC.

AC2 = AM2 + CM2 – 2 * AM * CM * Cos1200 = 36 + 36 – 2 * 6 * 6 * (-1 / 2) = 72 + 36 = 108.

AC = 6 * √3 cm.

| AC | = AC = 6 * √3 cm.

Answer: The module of the AB vector is 12 cm, and the AC vector is 6 * √3 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.