The angle at the apex of an isosceles triangle is 30 degrees; the height is lowered to the lateral side.

The angle at the apex of an isosceles triangle is 30 degrees; the height is lowered to the lateral side. find the angle between this height and the base. answers that can be: 1) 15 degrees 2) 45 degrees 3) 75 degrees 4) 20 degrees 5) 65 degrees

Since, by condition, the triangle ABC is isosceles, then its angles at the base of the AC are equal.

Angle BAC = BCA = (180 – ABC) / 2 = (180 – 30) / 2 = 150/2 = 75.

Triangle AНС is rectangular, since AH is the height of triangle ABC.

Then in a right-angled triangle AНС the angle СAН = (180 – AНС – СAН) = (180 – 90 – 75) = 15.

Answer: The angle between the height and the base is 15.