Question

В треугольнике АВС известно ,что угол с =90 °,АК-биссектриса,ВАК=18°.найдите углы АКСи АВСпожалуйста добавьте в решение рисунок и что данобуду оч рада и поставлю оценку (лучший ответ)заранее спасибо

Answer 1

Угол А=18*2=36 градусов 
угол КАС=18 градусов
180-18-90=72 градуса - угол АКС
180-90-36=54 градуса - угол АВС
Прости фотку не получилась сделать

Answer 2

Triangle ABC Angle Calculation

To solve for the angles AKS and ABC in triangle ABC, we can use the given information and trigonometric principles.

Given: - Angle C = 90° - AK is the bisector of angle A - Angle BAK = 18°

Solution:

First, let's draw the triangle ABC and label the given angles and sides.

         A
        /|
       / |
  AK /  | BC
     /   |
    /____|
   B     C

Now, let's calculate the angles AKS and ABC.

1. Angle BAC: - Since AK is the bisector of angle A, we can use the angle bisector theorem to find the measure of angle BAC. - The angle bisector theorem states that the angle bisector divides the opposite side in the ratio of the adjacent sides. - Using the theorem, we can calculate the measure of angle BAC.

2. Angle ABC: - Since angle BAC and angle BAK are known, we can calculate the measure of angle ABC using the fact that the sum of angles in a triangle is 180°.

3. Angle AKS: - To find the measure of angle AKS, we can use the fact that the sum of angles in a triangle is 180°.

Calculation:

1. Angle BAC: - Using the angle bisector theorem, we can calculate the measure of angle BAC. - Let's denote the measure of angle BAC as x. - According to the angle bisector theorem, we have: - (AB / AC) = (BK / KC) - We know that angle BAK = 18°, so angle KAC = 18° as well. - Therefore, angle BAC = 2 * 18° = 36°.

2. Angle ABC: - Since angle BAC = 36° and angle C = 90°, we can calculate angle ABC using the fact that the sum of angles in a triangle is 180°. - Angle ABC = 180° - 90° - 36° = 54°.

3. Angle AKS: - Since angle C = 90° and angle ABC = 54°, we can calculate angle AKS using the fact that the sum of angles in a triangle is 180°. - Angle AKS = 180° - 90° - 54° = 36°.

Conclusion:

- Angle BAC: 36° - Angle ABC: 54° - Angle AKS: 36°

This completes the calculation of the angles in triangle ABC.