We know

“the Pythagorean theorem or Pythagoras’ theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.”

First, we can use the Pythagorean theorem to find the length of side AC: <div>

•AC² = AB² + BC²- 2(AB)(BC) cos(A)

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•AC² = 8² + 10² – 2(8)(10) (cos(60))

•AC² = 164

•AC = √(164) = 2√(41)

<div>Next, we can use the fact that AD is the height of triangle ABC, and that triangle ABD is a 30-60-90 triangle, to find the length of AD:
•AD = AB/2 × √(3)</div><div>

•AD = 4 √(3)

Therefore, the length of segment AD is 4√(3) units.

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• This reply was modified 1 year, 2 months ago by  Daniel Die.