Question

Rezolvati complet. Coroana

Answer 1

a) AD=AP=4 cm

=> $\Delta$ APD isoscel

=> <APD=[180°-(60°+90°)]/2

=> <APD=(180°-150°):2

=> <APD=30°:2

=> <APD=15°

<=> <DPB=60°-15°

<=> <DPB=45°

b) m(<BDP)=45°-15°=30°

=> m(<ADM)=15°

=> m(<AMD)=180°-(90°+15°)

=> m(<AMD)=75°

=>

$AM=AD×~ctg(\angle AMD)\\AM=4×~ctg(75°)\\AM=4× ~ctg(30°+45°)\\\\AM=4×\frac{ctg(30°)+ctg(45°)-1}{ctg(30°)+(ctg(45)}\\\\AM=4×\frac{\sqrt{3}-1}{\sqrt{3}+1}\\\\AM=4×\frac{(\sqrt{3}-1)²}{2}\\\\AM=4×\frac{4-2\sqrt{3}}{2}\\\\AM=4×(2-\sqrt{3})\text{ cm}$