Question

calculati aria unui triunghi dreptunghic ABC, stiind ca inaltimea AD=4cm si măsura unghiului c =15
Ajutor, e urgent. ❤️

Answer 1

mai intai aflam valori pentru sin15 si cos15

pornim de la cos 30=2cos^2(15)-1=1-2sin^2(15)

cos^2(15)=[cos30+1]/2

sin^2(15) =[1- cos30]/2

deci

cos^2(15)=[cos30+1]/2=rad3/2+1/2=(rad3+2)/4

sin^2(15) =[1- cos30]/2=(2-rad3)/4

in triunghiul CDA aplic

sin 15=AD/AC AC=AD/sin15=16/(2-rad3)

CD=rad(AC^2-AD^2)=4rad15/(2-rad3)

teorema inaltimii

AD^2=CD*CB DB=AD^2/CD=16*(2-rad3)/4rad15=4*(2-rad3)/rad15

BC=CD+BD=4rad15/(2-rad3)+4*(2-rad3)/rad15

iar Aria=BC*AD/2