Question

How do you do this problem? Please explain.

Answer 1

Answer: 8.632

Explanation:

First, you need to find the length of AE. Since ΔAEC is a right triangle, we can use:

`sin\ C=(AE)/(AC)\\\\\\sin\ 50 = (AE)/(5)\\\\\\5\ sin\ 50=AE\\\\3.83=AE`

Next, Use Heron's formula to find the Area of ΔADE.

• AE = 3.83
• ED = 6
• AD = 9

Heron's formula is:

`A=√(s(s-a)(s-b)(s-c))\quad \text{where}\ s = (a+b+c)/(2)\\\\s=(AE+ED+AD)/(2)=(3.83+6+9)/(2)=(18.83)/(2)=9.415\\\\A=√(9.415(9.415-3.83)(9.415-6)(9.415-9))\\\\.\quad=√(9.415(5.585)(3.415)(0.415))\\\\.\quad=√(74.519)\\\\.\quad=8.632`