In the ABC triangle, the angle C is 90 degrees, the angle B is 65 degrees. CD is the height.

In the ABC triangle, the angle C is 90 degrees, the angle B is 65 degrees. CD is the height. find the corners of the triangle ACD.

In the ABC triangle it is known:

Angle C = 90 °;
Angle B = 65 °;
CD is the height of the triangle ABC.
Find the angles of the triangle ACD.

1) Find the angle A of the triangle ABC.

Angle A = 180 ° – angle C – angle B = 180 ° – 90 ° – 65 ° = 90 ° – 65 ° = 90 ° – 60 ° – 5 ° = 30 ° – 5 ° = 25 °;

2) Consider a triangle ACD with a right angle D.

The 2 angles of the triangle ACD are known.

Angle D = 90 °;

Angle A = 25 °;

Angle C = 180 ° – angle D – angle A = 180 ° – 90 ° – 25 ° = 90 ° – 25 ° = 90 ° – 20 ° – 5 ° = 70 ° – 5 ° = 65 °.

Answer: the angles of the triangle ACD are equal: angle D = 90 °, angle A = 25 °, angle C = 65 °.