In an isosceles triangle ABC AB = BC = 10 Sin angle B = 4/5, AH- height, find the segment CH.

Triangle ABH is rectangular since AH is the height of triangle ABC.

In a right-angled triangle ABC, we determine the length of the leg AH

SinАВН = АН / АВ.

AH = AB * SinABH = 10 * (4/5) = 8 cm.

By the Pythagorean theorem in a right-angled triangle ABH, we determine the length of the leg BH.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 100 – 64 = 36.

BH = 6 cm.

Since the triangle ABC is isosceles, then BC = AB = 10 cm.

Then the length of the segment СН = ВС – ВН = 10 – 6 = 4 cm.

Answer: The length of the CH segment is 4 cm.