In an isosceles triangle, one of the angles is 120 degrees. The base of the bisector of this angle is 12 cm

In an isosceles triangle, one of the angles is 120 degrees. The base of the bisector of this angle is 12 cm from one of the sides of the triangle. Find the base of the isosceles triangle.

1. Let’s designate the vertices of the triangle by symbols A, B, C. АС – base. ВН – bisector. НK – perpendicular to the BC side. Angle B = 120 °

2. The angles at the base of the speaker are equal:

Angle A = angle C = (180 ° – 120 °) / 2 = 30 °.

3. In the KCH triangle, the НK leg is opposite an angle of 30 °. Therefore, the CH hypotenuse is twice its length:

CH = НK x 2 = 12 x 2 = 24 cm.

4. The bisector is also the median and divides the base into two equal parts. That’s why,

AC = CH x 2 = 24 x 2 = 48 cm.

Answer: The length of the base of the speaker is 48 cm.