Răspuns:
a) 3 cm
b) 33 cm^2
c) 3/5
Explicație pas cu pas:
[tex]\displaystyle \textrm{a)Fie } E \in [AB] \textrm{ a. i. } DE \parallel BC \\ \\ EB = 7 \: cm\\ \\ ED = 5\:cm \\ \\ AB = AE + EB \implies AE = AB - EB = 15\:cm-7\:cm = 8\:cm\\ \\ \textrm{In } \triangle AED \textrm{ isoscel avem: }\\ \\ p = \frac{5+5+8}{2} = \frac{18}{2} = 9\:cm\\ \\ A = \sqrt{p(p-8)(p-5)(p-5)} = \sqrt{9}\cdot \sqrt{1}\cdot \sqrt{4}\cdot \sqrt{4} = 3\cdot 4 = 12\:cm^2 = \frac{h\cdot 8}{2} \\ \\ 4h = 12\\ \\ \boxed{h = 3 \:cm}\\ \\ \textrm{b)}\\ \\ A_{trapez} = \frac{3\cdot (15+7)}{2} = 3\cdot\frac{22}{2} = 3\cdot 11 = \boxed{33\:cm^2}\\ \\ \textrm{c) Fie }F = pr_{AB} C \\ \\ CF = h = 3\:cm\\ \\ \angle ABC = \angle FBC\\ \\ \sin{ABC} = \sin{FBC} \\ \\ \textrm{In triunghiul dreptunghic FBC avem:}\\ \\ \sin{FBC} = \frac{CF}{CB} =\boxed{ \frac{3}{5}}[/tex]
