Question

In ABC, a = 13,b=21, and c = 27. Find mA.

Answer 1

Answer:

Step-by-step explanation:

a = 13  ; b = 21  ; c = 27

S = (a + b + c)/2

   $= \dfrac{13+21+27}{2}\\\\=\dfrac{61}{2}\\\\= 30.5$

s- a = 30.5 - 13 = 17.5

s - b = 30.5 - 21 = 9.5

s  -c = 30.5 - 27 = 3.5

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

        $= \sqrt{30.5*17.5*9.5*3.5}\\\\=\sqrt{17747.1875} \\\\=133.21\\\\=133$

$\dfrac{cbSin \ A}{2}=133\\\\\dfrac{27*21*Sin A}{2}=133\\\\Sin \ A = \dfrac{133*2}{27*21}\\\\Sin \ A = 0.4691\\\\A = Sin^{-1} \ 0.4691$

A = 27°