In an isosceles triangle ABC, the base AC = 4, sinA = 2√2 / 3 Find the line segment connecting

In an isosceles triangle ABC, the base AC = 4, sinA = 2√2 / 3 Find the line segment connecting the midpoints of the AC and BC sides.

Since the points K and M are the midpoints of the sides BC and AC, the KM segment is the middle line of the triangle ABC.

Let’s build the height BM, which is also the median in an isosceles triangle, then AM = AC / 2 = 4/2 = 2 cm.

Determine the cosine of the angle BAC.

Cos2BAC = 1 – Sin2BAC = 1 – 8/9 = 1/9.

CosBAC = 1/3.

Then, in a right-angled triangle ABM, we determine the length of the hypotenuse AB.

AB = AM / CosBAC = 2 / (1/3) = 6 cm.

Since KM is the middle line of the triangle, then KM = AB / 2 = 6/2 = 3 cm.

Answer: The length of the KM segment is 3 cm.