Question

Помогите:) В тругольнике АБС проведена высота АН и биссектриса АЛ, при этом точка Л лежит на отрзке БН. Угол НАЛ равен 26 градусам, а АЛ=БЛ.Найдите угол Б треугольника АБС.Ответ дайте в градусах.

Answer 1

1)АЛН=АНЛ-ЛАН=90-26=64

2)Т.К. АЛН и АЛБ смежные углы то АБЛ=180-64=116

3)Т.К. АЛ=ЛБ то треугольник АЛБ-равностороний следовательно ЛАБ=АБЛ

  сумма всех углов треугольника = 180 тогда можно составить уравнение(х-угол ЛАБ или АБЛ):

2х+116=180

2х=64

х=32

Ответ: 32

Answer 2

ΔAHL- прямоугольный, поскольку АН- высота.

Угол АLH=180-(90+26)=64⁰

Угол BLA=180-64=116⁰, как смежный с углом  АLH

Δ BLA равнобедренный, значит

Угол В=(180-116)/2=32⁰

 

Как "Лучшее решение" не забудь отметить, ОК?!... ;)))

Answer 3

Triangle ABC and Angle B

To find the angle B in triangle ABC, we need to use the given information about the height AN and the bisector AL.

Let's analyze the given information step by step:

1. Triangle ABC: We have triangle ABC, where AB and AC are the sides, and BC is the base.

2. Height AN: A height is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. In this case, AN is the height of triangle ABC, drawn from vertex A to side BC.

3. Bisector AL: A bisector is a line or line segment that divides an angle into two equal angles. In this case, AL is the bisector of angle A in triangle ABC.

4. Point L lies on segment BN: The point L lies on the segment BN, which means it is a point on the line segment BN.

5. Angle NAL: The angle NAL is given as 26 degrees.

6. AL = BL: The length of AL is equal to the length of BL.

To find angle B, we can use the fact that AL = BL and the angle NAL is given as 26 degrees. Since AL = BL, angle BAL is also 26 degrees. And since AL is the bisector of angle A, angle B must be equal to angle BAL.

Therefore, angle B in triangle ABC is 26 degrees.

Please let me know if there is anything else I can help you with!