The two sides of the triangle are 20cm and 18cm, respectively, and the outer angle at their common

The two sides of the triangle are 20cm and 18cm, respectively, and the outer angle at their common vertex is 150 degrees. Find the height of the triangle to the 20cm side.

The sum of adjacent angles is 180 °, which means that the internal angle at the common vertex for the two known sides is 180 ° – 150 ° = 30 °. Knowing the two sides of the triangle and the angle between them, we can find the area:

S = 0.5 * a * b * sin α = 0.5 * 20 * 18 * sin 30 ° = 90 cm2.

On the other hand, the area of a triangle is half the product of the side and the height drawn to that side:

S = 0.5 * a * ha.

Hence:

ha = 2 * S / a = 2 * 90/20 = 9 cm – the height of the triangle drawn to the side equal to 20 cm.