Isosceles Triangle 80-80-20

Isosceles Triangle 80-80-20

Vivek updated 1 month, 1 week ago 2 Members · 6 Posts
Puzzles
- geometry
Puzzle Prime

Administrator
October 22, 2020 at 7:52 am

You are given an isosceles triangle ABC, ∠CAB = ∠ABC = 80°. Point D belongs to the side BC, so that AB = CD. Find the measure of angle ∠DAB.
Vivek

Member
October 22, 2020 at 2:14 pm

70 degrees. Using sine and cosine law of triangles, and standard trigonometric identities.
- Puzzle Prime
  
  Administrator
  October 22, 2020 at 2:40 pm
  
  Yeah, trigonometry works well for this problem. Try to find the “pretty” solution now though:)
- Vivek
  
  Member
  October 23, 2020 at 8:20 pm
  
  Got it!
- Puzzle Prime
  
  Administrator
  October 23, 2020 at 8:26 pm
  
  Wow, I have never seen this solution before, good job! There are (at least) 2 other solutions involving equilateral triangles:)
- Vivek
  
  Member
  October 23, 2020 at 8:40 pm
  
  Before your “pretty solution -clue”, I got that through lots of equations , changing 1/2 to sin 30 and the like. haha..This is cool! 🙂