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The vertices of triangle are a(-1,-1),b(2,3),c(4,2),then the greatest angle of triangle is
Asked by Njishang | 20 Mar, 2019, 21:48: PM
answered-by-expert Expert Answer
Th triangle is plotted as per the given vertices.
 
Area of Δ = (1/2)[ -1(2-3)+4(3+1)+2(-1-2) ] = 11/2 sq.units
 
length of AC = b = begin mathsize 12px style square root of left parenthesis negative 1 minus 2 right parenthesis squared plus left parenthesis negative 1 minus 3 right parenthesis squared end root space equals space 5 space u n i t s end style
length of BC = a = begin mathsize 12px style square root of open parentheses 4 minus 2 close parentheses squared plus open parentheses 2 minus 3 close parentheses squared end root space equals space square root of 5 space u n i t s end style
we have ,  (1/2)a b sin C = Δ   ,   hence sin C  = 2Δ /(a b )  =  11/(5√5) = 0.984
 
hence angle C = sin-1 (0.984) ≈ 80° .   since C is obtuse angle, angle C = 180 -80 = 100°
Answered by Thiyagarajan K | 21 Mar, 2019, 07:47: AM

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