In an isosceles triangle ABC, the height BD is drawn to the base of the AC

In an isosceles triangle ABC, the height BD is drawn to the base of the AC. The length of the height is 12.5 cm, the length of the lateral side is 25 cm. Determine the angles of this triangle.

1. In accordance with the properties of a right-angled triangle, the ВD leg, which is half the length of the hypotenuse AB (25: 2 = 15 cm), is opposite the angle BAC equal to 30 °.

2. According to the properties of an isosceles triangle, the angles at the base of the AC are equal, that is, the angle BAC = angle ACB = 30 °.

3. Angle ABC = 180 ° – 30 ° – 30 ° = 120 °.

Answer: angle ABC = 120 °, angle BAC = angle ACB = 30 °.