Given: ABCD is a rhombus,

AB = 6, and m∠A=60°
Find: The height.

the height is 5.2 units

ur wrong

The height is 3 times the square root of 3 or square root 27 simplified

the answer is 3 root 3

u see using the opposite leg from 60 degree thereom and also using the pythagorean thrm u should get 3 root 3 to be the answer.
ps. ur welcome ppl

3 root 3 is the correct answer

Height is 5.20 units. This is because the area of the rhombus divided by the base of the rhombus is equal to the height of said rhombus.

To find the height of the rhombus, you need to use the formula for the area of a rhombus. The formula is:

Area = (diagonal1 * diagonal2) / 2

In a rhombus, the diagonals are perpendicular bisectors of each other, which means they intersect at a right angle.

First, let's find the length of the diagonals using the given information. Since we know AB = 6, we can find the length of the diagonals using the properties of a rhombus.

In a rhombus, the diagonals are congruent. Let's call the length of both diagonals d.

Since m∠A = 60°, we can see that triangle ABD is a 30-60-90 triangle.

In a 30-60-90 triangle, the lengths of the sides are proportional to the ratio 1 : √3 : 2.

So, AB / BD = 1 / √3.

Simplifying, we get BD = AB√3 = 6√3.

Since the diagonals are congruent, we have: d = 2 * BD = 12√3.

Now, let's substitute the values in the formula for the area of the rhombus:

Area = (diagonal1 * diagonal2) / 2.

Area = (12√3 * 12√3) / 2 = (144 * 3) / 2 = 432 / 2 = 216.

The area of the rhombus is 216.

To find the height of the rhombus, we can divide the area by the length of one side.

Height = Area / side length.

Height = 216 / 6 = 36.

Therefore, the height of the rhombus is 36 units.

6root6

AD is also 6, so the height is 6 sin60°