Answer:
The correct option is C ) 109.5°
Therefore,
[tex]m\angle E=109.5\°[/tex]
Step-by-step explanation:
Given:
In Triangle DEF
d = 10
e = 18
f = 12
To Find
angle E = ?
Solution:
In Triangle DEF , Cosine Rule says
[tex]\cos E=\dfrac{f^{2}+d^{2}-e^{2}}{2fd}[/tex]
Substituting the values we get
[tex]\cos E=\dfrac{12^{2}+10^{2}-18^{2}}{2\times 12\times 10}[/tex]
[tex]\cos E=\dfrac{-80}{240}=-\dfrac{1}{3}[/tex]
Therefore,
[tex]\angle E=\cos^{-1}(-0.3333)[/tex]
[tex]m\angle E=109.5\°[/tex] ............As it is in Second Quadrant
Therefore,
[tex]m\angle E=109.5\°[/tex]
