Question

Fie trapezul dreptunghic ABCD cu m(A)=90 grade, AB||CD, AB>CD. Stiind ca m(CAB)=60 grade si AC perpendicular pe BC, aratati ca AB=4CD.

Answer 1

[tex]sin30= \frac{1}{2} [/tex]
[tex]adica \frac{AE}{AC} = \frac{1}{2} [/tex]
[tex] \frac{AC}{AB} = \frac{1}{2} mai stim si ca AE=CD [/tex]
[tex] \frac{AE}{AC} = \frac{AC}{AB} = \frac{1}{2} mai stim si ca AC=2*AE=2*CD[/tex]
[tex]AC = \frac{AB}{2} [/tex]
[tex]2*CD= \frac{AB}{2} ceea ce rezulta ca 4*CD=AB adica AB=4CD.[/tex]