Find the height in an isosceles triangle with a side of 14 cm and an angle of 150 degrees.

An angle of 150 degrees is the angle against the base, since it is greater than 90.

Since the condition does not indicate the length of which height to find, we define both heights.

Let’s draw the height to the side of the triangle.

Angle ABK and ABC are adjacent angles, then angle ABK = 180 – 150 = 30.

In a right-angled triangle ABK, the height of AK lies against an angle of 30, then AK = AB / 2 = 14/2 = 7 cm.

Let’s draw the height to the base of the speaker.

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

Then the angle ABN in a right-angled triangle ABN is equal to: ABN = ABC / 2 = 150/2 = 75.

From the right-angled triangle ABH, we determine the size of the leg BH.

Cos75 = BH / AB.

BH = AB * Cos75 = 14 * 0.259 = 3.626 cm.

Answer: The length of the height to the side is 7 cm, to the base of the speaker is 3.626 cm.