Triangle DEF is such that DF=8cm,EF=5.5cm and its area is 11 root2 cm^2. Find angle EFD.
Area = 0.5*Ef*DF*sinF = 11 cm^2.
0.5*5.5*8*sinF = 11
22*sinF = 11
sinF = 0.5
F = 30o.
To find angle EFD, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base of the triangle is EF and the height is DF. Let's plug in the given values:
11√2 cm^2 = (1/2) * EF * DF
Rearranging the equation, we get:
EF * DF = 2 * (11√2 cm^2)
Substituting the given values, we have:
5.5cm * 8cm = 2 * (11√2 cm^2)
44 = 22√2
Dividing both sides by 22, we get:
2 = √2
Now, we need to find the value of √2. To do this, we can square both sides of the equation:
(2)^2 = (√2)^2
4 = 2
Since the equation is not true, it means there is no solution for angle EFD that satisfies the given conditions.