Question

Помагите СРОЧНО решить!!!! В треугольнике АВС проведена высота АН и биссектриса АL, при этом точка L лежит на отрезке ВН. Угол НАL равен 26 ,а АL=ВL. Найдите угол В треугольника АВС.Ответ дайте в градусах.

Answer 1

Из треугольника АLН получим -угол АLH=90-26=64. Тогда угол ВLА=180-64=116. Треугольник АВL равнобедренный (АL=ВL по условию). Значит углы при основании равны (угол АВL=углу ВАL). Пусть каждый из них равен Х. Тогда в треугольнике АВL получим  2Х+ угол ВLА=180. Отсюда Х=32.

Answer 2

Problem Analysis

We are given a triangle ABC with the altitude AN and the bisector AL, where point L lies on the segment HN. We are also given that angle NAL is 26 degrees and AL = BL. We need to find angle B in triangle ABC.

Solution

To find angle B, we can use the properties of a triangle and the given information.

Let's denote angle B as x.

Since AL = BL, we can conclude that angle BAL is also x degrees.

Since AL is the bisector of angle B, we know that angle BAL is equal to angle BAC.

Therefore, angle BAC is also x degrees.

Since angle NAL is 26 degrees, we can conclude that angle BAN is also 26 degrees.

Now, we can use the fact that the sum of angles in a triangle is 180 degrees to find angle B.

The sum of angles in triangle ABC is given by:

angle BAC + angle BCA + angle ABC = 180 degrees

Substituting the values we know:

x + 26 + x = 180

Simplifying the equation:

2x + 26 = 180

Subtracting 26 from both sides:

2x = 154

Dividing both sides by 2:

x = 77

Therefore, angle B in triangle ABC is 77 degrees.

Answer

The angle B in triangle ABC is 77 degrees.