In a right-angled triangle, the angle between the height and the median is 14º,

| April 5, 2021 | education

In a right-angled triangle, the angle between the height and the median is 14º, drawn from the top of the right angle. Find the smallest angle of the triangle.

Let ABC be a given triangle (angle C = 90 °). CH – height, CM – median, angle MСН = 14 °.

Consider a triangle MCH: angle H = 90 ° (CH – height). Find the value of the СMН angle:

СМН = 180 ° – (14 ° + 90 °) = 76 ° (the sum of the angles in the triangle is 180 °).

The angles CMA and CMН are adjacent, which means that the angle CMA = 180 ° – 76 ° = 104 °.

In a triangle AMC: AM = CM (in a right-angled triangle, the median is half the hypotenuse). This means that the triangle AMC is isosceles, the angle of the MAC is equal to the angle MCA = (180 ° – 104 °): 2 = 38 ° (angle A of the triangle ABC).

In triangle ABC: angle B = 180 ° – (90 ° + 38 °) = 52 °.

This means that the smallest angle of the triangle is 38 °.



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.