1 Answer

Fiery Phoenix · Answer 1 · 2023-05-01T22:06:18+0000

We will have the following:

First, we find the missing angle:

$A=180-40-49\Rightarrow A=91$

Second, we use the law of sines to calculate the missing sides "a" & "c", so

c:

$(c)/(\sin (40))=(13)/(\sin(49))\Rightarrow c=(13\sin(40))/(\sin(49))$
$\Rightarrow c=11.07212515\ldots$

a:

$(a)/(\sin(91))=(13)/(\sin(49))\Rightarrow a=(13\sin (91))/(\sin (49))$
$\Rightarrow a=17.22254544\ldots$

So:

$p=13+17.22254544+11.07212515\Rightarrow p\approx41$

So, the perimeter of the triangle is approximately 41 units.

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