# How do you find the area of triangle DEF given d=5.83, e=5.83, mangleF=48?

Jan 27, 2018

$A = 12.58 \setminus {\text{units}}^{2}$

#### Explanation:

We can find the area of a triangle using trigonometric functions, such as

$A = \frac{1}{2} \mathrm{de} \sin F$ in this case

$d = e = 5.83$

$F = 48$

$\therefore \sin {F}^{\circ} = 0.74$

$: A = \frac{1}{2} \cdot 5.83 \cdot 5.83 \cdot 0.74$

$A \approx 12.58 \setminus {\text{units}}^{2}$

Jan 27, 2018

Area $\triangle D E F \approx 12.629341$ sq units

#### Explanation:

Here we have $\triangle D E F$ given $\angle F = {48}^{o}$ and the sides opposite both $\angle D \mathmr{and} \angle E = 5.83$ units

So we have been given the lengths of two sides and the included angle. We can use the formuls below for the area of $\triangle D E F$

Area $\triangle D E F = \frac{1}{2} d e \sin F$
$= \frac{1}{2} \times 5.83 \times 5.83 \times \sin \left({48}^{o}\right)$

$\approx \frac{1}{2} \times 33.9889 \times 0.743145$

$\approx 12.629341$ sq units

NB: Since $\triangle D E F$ is Isosceles (since d=e) other methods could be used to solve this.