In an isosceles triangle, the side is twice its width. Find the corners of the triangle.

Let’s draw an isosceles triangle and denote it by ABC. The base is denoted as X, and the side as 2X. Let’s draw the height to the base of BD. The height of an isosceles triangle, drawn to the base, divides it into two equal right-angled triangles. The height will also be the median, so the AD segment will be equal to X / 2.

Consider a triangle ABD, it is rectangular. Find the angle BAD through the cosine

cos A = x / 2: 2x = 1/4.

If the cosine of the angle is 1/4, then the angle will be 75∘ (according to the Bradis table). Since the triangles are equal, the DCB angle is 75∘, respectively. Let’s go back to triangle ABC. The base angles are 75 рав. Subtracting the angles at the base from 180∘, we find the angle of the apex.

∠ABC = 180∘ – 2 × 75∘ = 30∘