In an isosceles triangle, the outside angle at the base is 150 degrees. Find the height dropped

In an isosceles triangle, the outside angle at the base is 150 degrees. Find the height dropped from the top to the base if the side is 7 cm.

Let us denote the triangle given by the condition ABC AB = BC, BH is the height drawn to the base of the AC.
By condition, the outer angle at the base is known, we find the inner angle ACB adjacent to it:
∠ АСВ = 180 ° – 150 ° = 30 °.
Consider a right-angled triangle BAC, in which we know the hypotenuse BC = 7 (the side of the triangle) and one of the acute angles 30 °.
The height of the HV is located opposite the angle ACB = 30 °, which means it is equal to half of the hypotenuse of the BC:
ВН = 1/2 * ВС = 3.5.
Answer: the height is 3.5