Question

fie ABCD un trapez dreptungh,[AB] | | [CD] ,m(<A)=90° ,AB=24 cm ,CD=16 cm si tg (<ABC)=3 supra 4 sa se calculeze a) aria trapezului b) distanta de la A la dreapta BC

Answer 1

vezi atasament
n-am figurat d(A, BC), ci doar triunghiul ABC

Answer 2

Fie CE⊥AB
EC=AD-inaltime
AE=DC=16 cm
ED=AB-AE=24-16=8 cm
In ΔCEB, m(∡CEB)=90⁰=>tgB=CE/EB <=>3/4=CE/8=>CE=(8*3)/4=24/4=6 cm
A=[(B+b)*h]/2=[(AB+DC)*EC]/2=[(24+16)*6]/2=(40*6)/2=40*3=120 cm²
d(A,BC)=AC
m(∡CAE)=m(∡DAE)/2=90⁰/2=45⁰
In ΔAEC , m(∡AEC)=90⁰ =>sinA=CE/AC<=>sin45⁰=6/AC<=>√2/2=6/AC=>AC=(6*2)/√2=12/√2=12√2/2=6√2=8,46 cm