In a triangle, one of the sides is equal to a, the adjacent angles are 30 ° and 60 ° Find the height of the triangle drawn to this side.

Let’s determine what the remaining angle in our figure will equal if the other two are equal to 30 ° and 60 °:

180 – 30 – 60 = 90.

That is, the triangle turns out to be rectangular.

Let’s determine what the leg will be equal to, which lies opposite an angle of 30 °:

a * sin 30 ° = a * 1/2 = a / 2.

Let’s determine what the leg will be equal to, which lies opposite an angle of 60 °:

a * sin 60 ° = a * √3 / 2 = a√3 / 2.

Let’s determine what the area will be equal to:

1/2 * a / 2 * a√3 / 2 = a ^ 2√3 / 8.

Let’s determine what the height is equal to:

a ^ 2√3 / 8 * 2: a = a√3 / 4.

Answer: a√3 / 4.