Given triangle ABC is isosceles, AB-base is equal to the root of 2, angle A = 30 heights to find the perimeter.

By the condition of the task, the triangle is isosceles, and the base is designated AB, which means that the angle B will be equal to the angle A.

Determine how many degrees the angle will be expressed, which lies opposite the base:

180 – 30 * 2 = 180 – 60 = 120.

Let us determine what the lateral side will equal, using the theorem of sines known from the school course, if we know from the condition that the base is √2:

√2: √3 / 2 = AC: 1/2;

AC = √2 / √3.

Let’s define the perimeter:

√2 + 2√2 / √3 = √2 (1 + 2 / √3).

Answer: √2 (1 + 2 / √3).