Triangle abc is equilateral. find the height of bd

Since ABC is equilateral, all 3 sides have equal length. side AC is 8 units since side BC is 8 units.

Line BD is placed in the middle, making D the midpoint of side AC.

knowing this information we can determine that the length of DC is 4 units (half of AC)

since triangle BDC is a right triangle, we can use the side lengths in the pythagorean theorem to find the length of BD

a²+b²=c² where a & b = legs of triangle , and c= hypotenuse (longest side)

we are given the hypotenuse and found one leg so we can plug our values into the equation to find the third

4² + b²= 8²

16 + b² = 64

b² = 48

b =

b= 4√3 or about 6.928 units

hope this helped