Question

5.(2 бали) Кут між бісектрисою BL і катетом АC прямокутного трикутника АВС (< С = 90°) дорівнює 55°. Знайдіть гострі кути трикутника АВС 7.(3 бали) У трикутнику АВС кут С дорівнює 90°, а кут В дорівнює 60°. На катеті АС відкладено відрізок СD рівний СВ. Знайдіть кути трикутника АВD.помогите пж срочно нужно умоляю сегодня сдать даю 100 балов за две задачи

Answer 1

ΔВСL - прямокутний, ∠СВL=90-55=35°

∠АВС=35*2=70° за визначенням бісектриси

∠А=90-70=20°

Відповідь: 70°   20°

∠А=90-60=30°;  

ΔСВD - рівнобедрений за умовою,  ∠CDB=∠CBD=45°

∠DАВ=60-45=15°

∠ADB=180-30-15=135°

Відповідь: 135°   30°   15°

Answer 2

Task 5:

To find the acute angles of triangle ABC, we are given that the angle between the bisector BL and the cathetus AC of right triangle ABC (with angle C = 90°) is 55°.

Let's denote the acute angles of triangle ABC as angle A and angle B.

To find angle A, we can use the fact that the sum of the angles in a triangle is 180°. Since angle C is 90° and angle B is 55°, we can calculate angle A as follows:

angle A = 180° - angle B - angle C

Substituting the given values:

angle A = 180° - 55° - 90°

Simplifying:

angle A = 35°

Therefore, angle A of triangle ABC is 35°.

To find angle B, we can use the fact that the sum of the angles in a triangle is 180°. Since angle C is 90° and angle A is 35°, we can calculate angle B as follows:

angle B = 180° - angle A - angle C

Substituting the given values:

angle B = 180° - 35° - 90°

Simplifying:

angle B = 55°

Therefore, angle B of triangle ABC is 55°.

In summary, the acute angles of triangle ABC are angle A = 35° and angle B = 55°.

Task 7:

To find the angles of triangle AVD, we are given that angle C of triangle ABC is 90°, angle B is 60°, and segment CD is equal to segment CV.

Let's denote the angles of triangle AVD as angle A, angle V, and angle D.

Since angle C of triangle ABC is 90°, angle A of triangle AVD is also 90°.

To find angle V, we can use the fact that the sum of the angles in a triangle is 180°. Since angle A is 90° and angle D is unknown, we can calculate angle V as follows:

angle V = 180° - angle A - angle D

Substituting the given values:

angle V = 180° - 90° - angle D

Simplifying:

angle V = 90° - angle D

Since angle B of triangle ABC is 60°, angle V of triangle AVD is equal to angle B:

angle V = angle B = 60°

Therefore, we have:

60° = 90° - angle D

Simplifying:

angle D = 90° - 60°

angle D = 30°

In summary, the angles of triangle AVD are angle A = 90°, angle V = 60°, and angle D = 30°.

I hope this helps! Let me know if you have any further questions.