The measure of a vertex angle of an isosceles triangle is 120°, the length of a leg is 8 cm. find the length of a diameter of the circle circumscribed about this triangle.

16 cm

Step-by-step explanation:

Consider isosceles triangle ABC with vertex angle ACB of 120° and legs AC=CB=8 cm.

CD is the median of the triangle ABC. Since triangle ABC is isosceles triangle, then median CD is also angle ACB bisector and is the height drawn to the base AB. Thus,

∠DCB=60°

Consider triangle OBC. This triangle is isoscels triangle, because OC=OB=R of the circumscribed about  triangle ABC circle. Thus,

∠OCB=∠OBC=60°

So, ∠COB=180°-60°-60°=60°.

Therefore, triangle OCB is equilateral triangle.

This gives that

OC+OB=BC=8 cm.

The diameter of the circumscribed circle is 16 cm.

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.