The largest interior angle of a kite is 140 °. Side measures are 1.6 m and 1.2 m. Determine the shortest diagonal line kite.

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Let ABCD is ite in which , AB=1.2 and BC=16 and angle ABC= 140

join A to C

In triangle ABC , by sine law

`sin(140)/(AC)=sin(angleB)/1.2=sin (angleA)/1.6`

`` also

`angleA+angle B=40`

`angleB=40-angle A`

`sin(angle B)=sin(40-angleA)=sin(40)cos(A)-cos(A)sin(angleA)`

`(.64 cos(A)-.77sin(A))/1.2=sin(A)/1.6`

`16 cos(A)=38 sin(A)`

`` `tan(A)=16/38`

`A=22.83^o`

join BD ,BD is perpendicular to AC . AC bsect BD say at M .

In triangle AMB

`sin(22.83)=(BM)/1.2`

`BM=1.2xx sin(22.83)=.47`

`Thus`

`BD=2xxBM=2xx.47=.94` m

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