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

Question

3202 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-27T01:53:10

$A=12.58 \ "units"^2$

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

$A=1/2desinF$ in this case

$d=e=5.83$

$F=48$

$:.sinF^@=0.74$

$:A=1/2*5.83*5.83*0.74$

$A~~12.58 \ "units"^2$

Answer 2 · 2018-01-27T01:55:13

Area $triangle DEF approx 12.629341$ sq units

Here we have $triangle DEF$ given $angle F = 48^o$ and the sides opposite both $angle D and angle E = 5.83$ 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 $triangle DEF$

Area $triangle DEF = 1/2 d e sinF$
$=1/2xx5.83xx5.83 xx sin(48^o)$

$approx 1/2 xx 33.9889 xx 0.743145$

$approx 12.629341$ sq units

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

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