Answer: Area of ∆ADF is 42.44 m² .
Step-by-step explanation:
Since we have given that
AD = 14 m
m∠F = 90°
m∠D = 30°
We need to find the area of ∆ADF,
As we know the formula for " Area of triangle ":
[tex]Area=\frac{1}{2}\times b\times h[/tex]
For this we need to find the base and height of the given triangle.
We will use the "Trigonometric Ratio ":
[tex]\sin 60\textdegree=\frac{FA}{AD}\\\\\frac{\sqrt{3}}{2}=\frac{FA}{14}\\\\\frac{14}{2}\times \sqrt{3}=FA\\\\7\sqrt{3}=FA\\\\12.12\ m=FA[/tex]
Similarly, we will find the base.
[tex]\cos 60\textdegree=\frac{DF}{AD}\\\\\frac{1}{2}=\frac{DF}{14}\\\\DF=\frac{14}{2}=7[/tex]
Now, we will apply the formula for Area of triangle :
[tex]Area=\frac{1}{2}\times FA\times DF\\\\Area=\frac{1}{2}\times 12.12\times 7\\\\Area=42.435\\\\Area=42.44\ m^2[/tex]
Hence, Area of ∆ADF is 42.44 m² .
