Question

Given: △AFD, m∠F=90°
DF=7√3 , m∠D=30°
Find: Area of △AFD

Answer 1

Using the definition of the tangent function, you can find ...

... FA = DF·tan(30°) = (7√3)·(1/√3) = 7

Then the usual formula for triangle area can be used:

... Area = (1/2)bh = (1/2)·(7√3)(7)

... Area = (49/2)√3 square units

... ≈ 42.44 square units

Answer 2

We need to find the area of a triangle whose one side and two angles are given.

The area of $\triangle A FD$ is $43.44\ \text{unit}^2$.

In $\triangle A FD$

$\angle F=90^{\circ}$

$\angle D=30^{\circ}$

$DF=7\sqrt{3}$

From the trigonometric identities we have

$\tan D=\dfrac{A F}{DF}\\\Rightarrow A F=DF\tan D\\\Rightarrow A F=7\sqrt{3}\times \tan30^{\circ}=7\sqrt{3}\times \dfrac{1}{\sqrt{3}}\\\Rightarrow A F=7\ \text{units}$

Area of a triangle is given by

$A=\dfrac{1}{2}\times\text{Base}\times\text{Height}\\\Rightarrow A=\dfrac{1}{2}\times A F\times DF\\\Rightarrow A=\dfrac{1}{2}\times 7\times7\sqrt{3}\\\Rightarrow A=24.5\sqrt{3}=43.44\ \text{unit}^2$

The area of $\triangle A FD$ is $43.44\ \text{unit}^2$.

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