In an even triangle, the apex angle is 12 degrees lateral side = 7 cm find the length of the height

In an even triangle, the apex angle is 12 degrees lateral side = 7 cm find the length of the height drawn to the base of the triangle.

Since triangle ABC is isosceles, its height BH is also the median of the triangle and the bisector of angle B.

Then AH = CH = AC / 2 cm, angle ABH = ABC / 2 = 12/2 = 6 cm, and triangle ABH is rectangular.

Then, in a right-angled triangle ABH, BH = AB * CosABН = 7 * Cos6 = 6.96 cm.

If the angle B = 120, then in a right-angled triangle ABH the angle BAH = 90 – 60 = 30, then BH = AB / 2 = 7/2 = 3.5 cm.

Answer: The length of the height is 6.96 cm (3.5 cm).