Question

The angles of a ΔABCΔABC  are in the ratio 1:1:21:1:2  then the ratio of their sides is​

Answer 1

From cosine rule we have

⇒c

2

−2bccosA+b

2

−a

2

=0

let c

1

and c

2

be the roots of the above equation.

The sum of the roots = c

1

+c

2

=2bcosA

Now, sum of area of two triangle=Δ=Δ

1

+Δ

2

=

2

bc

1

sinA+bc

2

sinA

=

2

b(c

1

+c

2

)sinA

⇒△=b

2

cosAsinA=

2

b

2

sin2A

sry typing mistake plz understand icant domore

Answer 2

$\huge \fcolorbox{cyan}{skyblue}{Answer}$

$\sf{From \: cosine \: rule \: we \: have}$

$\sf{⇒c²−2bccosA+b²−a²=0 }$

$\sf{let \: c1 \: and \: c2 \: be \: the \: roots \: of \: the \: above \: equation.}$

$\sf{The \: sum \: of \: the \: roots = c1+cc =2bcosA}$

$\sf{Now, sum \: of \: area \: of \: two \: triangle=Δ= }$

⇒△=b²cosAsinA=2b²sin2A / 2

$\sf \purple{Swipe \: to \: see \: full \: solution}$