if a ,b,c are the lengths of sides BC ,CA,AB of a triangle ABC proof that

BC+CA+AB=0 and deduce that

a/sinA=b/sinB=c/sinC

refer r.d 25.1 ques 20 and pls answer fast pls of all ques that r asked

Question

if a ,b,c are the lengths of sides BC ,CA,AB of a triangle ABC
proof that
BC+CA+AB=0 and deduce that
a/sinA=b/sinB=c/sinC
refer r d 25 1 ques 20 and pls answer fast pls of all ques that
r asked

Ajanta Trivedi · Accepted Answer

in vector geometry

AB+BC+CA=(AB+BC)+CA=AC+CA=AC-CA=0

area of the triangle ABC with the sides a,b and c is given by:

Area= $b c \sin A = a b \sin C = a c \sin B$

dividing the whole equation by abc:

$\frac{b c \sin A}{a b c} = \frac{a b \sin C}{a b c} = \frac{a c \sin B}{a b c} \frac{\sin A}{a} = \frac{\sin C}{c} = \frac{\sin B}{b} \Rightarrow \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

if a ,b,c are the lengths of sides BC ,CA,AB of a triangle ABC proof that BC+CA+AB=0 and deduce that a/sinA=b/sinB=c/sinC refer r.d 25.1 ques 20 and pls answer fast pls of all ques that r asked

if a ,b,c are the lengths of sides BC ,CA,AB of a triangle ABC proof that

BC+CA+AB=0 and deduce that

a/sinA=b/sinB=c/sinC

refer r.d 25.1 ques 20 and pls answer fast pls of all ques that r asked