Answer: 8.632
Step-by-step explanation:
First, you need to find the length of AE. Since ΔAEC is a right triangle, we can use:
[tex]sin\ C=\dfrac{AE}{AC}\\\\\\sin\ 50 = \dfrac{AE}{5}\\\\\\5\ sin\ 50=AE\\\\3.83=AE[/tex]
Next, Use Heron's formula to find the Area of ΔADE.
Heron's formula is:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\quad \text{where}\ s = \dfrac{a+b+c}{2}\\\\s=\dfrac{AE+ED+AD}{2}=\dfrac{3.83+6+9}{2}=\dfrac{18.83}{2}=9.415\\\\A=\sqrt{9.415(9.415-3.83)(9.415-6)(9.415-9)}\\\\.\quad=\sqrt{9.415(5.585)(3.415)(0.415)}\\\\.\quad=\sqrt{74.519}\\\\.\quad=8.632[/tex]
