Question

Triunghiul ABC dreptunghic in A ,AC=radical3-1(doar 3 sub radical),tg B=2-radical3. Calculati cos C

Answer 1

tgB = AC / AB              ; ( √3 -1 ) /AB = 2 -√3 
AB = ( √3 -1 ) / ( 2 -√3) = = ( √3 -1 ) ·( 2 + √ 3 )   /  ( 2 -√3 ) ·(2 +√3 ) 
AB = √3+1 
BC² = (√3+1 )² +( √3 -1 )² = 3+ 2√3 +1 +3 - 2√3 +1 = 8
BC =√8 = √4 · √2 =2√ 2
cosC = AC/ BC = ( √3 -1 ) / 2√2 = ( √6  - √2 ) / 4 
C =75⁰