Question

Rombul ABCD , AC=12 BD=16 , Aflati sin ABC

Answer 1

Răspuns:

Explicație pas cu pas:

AC, BD diagonale, dar AC⊥BD. Fie AC∩BD=O.

Atunci ΔAOB dreptunghic in O cu AO=(1/2)·AC=6, iar BO=(1/2)·BD=8.

AB²=AO²+BO²=6²+8²=10², deci AB=10cm.

Aria(ABCD)=(1/2)·AC·BD=(1/2)·12·16=96cm².

dar Aria(ABCD)=AB·BC·sin(∡ABC), ⇒10·10·sin(∡ABC)=96 ⇒sin(∡ABC)=96/100=0,96.