Răspuns:
P = 420 cm; BE = 151,2 cm
Explicație pas cu pas:
[tex]\sin(C) = 0.8 = > \sin(C) = \frac{4}{5} \\ [/tex]
[tex]\sin(C) = \frac{AD}{AC} < = > \frac{60}{AC} = \frac{4}{5} \\AC = \frac{5 \times 60}{4} = > AC = 75 \: cm[/tex]
[tex]\sin(B) = \frac{AD}{AB} < = > \frac{60}{AB} = \frac{5}{13} \\ AB = \frac{60 \times 13}{5} = > AB = 156 \: cm[/tex]
DC² = AC² - AD² = 75² - 60² = 45²
→ DC = 45 cm
BD² = AB² - AD² = 156² - 60² = 144²
→ BD = 144 cm
BC = BD + DC = 144 + 45 = 189
→ BC = 189 cm
perimetrul (ABC) = AB + BC + AC = 156 + 189 + 75 = 420
→ P = 420 cm
[tex]\sin(C) = \frac{BE}{BC} < = > \frac{BE}{189} = \frac{4}{5} \\BE = \frac{189 \times 4}{5} = > BE = 151.2 \: cm[/tex]
