• Math

  trignometry

  Posted by Ganesh on June 23, 2023 at 11:53 pm

  In a triangle ABC, angle A is 60 degrees, side AB has a length of 8 units, and side BC has a length of 10 units. Let D be the foot of the perpendicular drawn from A to side BC. Find the length of segment AD.

  Dhwani replied 11 months ago 3 Members · 2 Replies
• 2 Replies

• 

  Daniel

  Member

  June 24, 2023 at 12:05 pm

  Helpful

  Up

  0

  Down

  Not Helpful

  ::

  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)

  <div>

  •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.

  </div></div></div>

  • This reply was modified 11 months ago by  Daniel Die.
• 

  Dhwani

  Member

  June 24, 2023 at 12:07 pm

  Helpful

  Up

  0

  Down

  Not Helpful

  ::

  I hope this might help you.

  

Log In to Reply