Question

Va rog
1) Sa se afle aria rombului abcd in care ac=30 si cos abd=8/17
2)sa se arate ca in orice dreptunghi abcd ac intersectat bd in o Aabo=Aado=1/4Aabcd
3)sa se afle aria rombului abcd in care se cunosc ab =10 si sin a=24/25

Answer 1

1.
ac=30   ⇒ ao=oc=30:2=15 
cos abd=8/17 
bo/ab =8/17
constatam ca 17²-8²=15²
bd=8x2=16
A=16x30/2=480/2=240

2
ducem om_I_ab
ducem on_I_ad
om=an =ad/2  ⇒ad=2om=2an
am=on=ab/2  ⇒ ab=2am=2on
Aabo=abxom/2=2on x om/2=on x om 
Aado=adxon/2=2om x on/2=om x on 
rezulta ca Aabo=Aado

3
sin a=24/25
ducem bm_I_ad   (inaltime in triunghiul abd)
sin a = bd/10
24/25 = bd/10
bd=10x24/25=9,6
A=10x9,6=96