Construct a triangle abc in which bc=5cm angle b=45 degree ab- ac=2.8cm Justify your construction

Dear Student,

Please find below the solution to the asked query:

We follow these steps to form our triangle ABC  :  given angle is $\angle \mathrm{B}$ = 45$°$ , BC =  5 cm and AB - AC  =  2.8 cm

Step 1 :  Draw a line BC =  5   cm

Step 2 :Take any radius (  Less than half of BC ) and center " B "  we draw a semicircle that intersect our line BC at "P " . With same radius take center "  P "  draw an arc that intersect our semicircle at " Q " And with same radius take center "  Q "  draw an arc that intersect our semicircle at " R " .

Step 3 :  With same radius take center "  Q "  and " R " draw two arcs that intersect each other at  " S " . Join line BS , that intersect our semicircle at " T "

Step 4 :   With same radius take center "  P "  and " T " draw two arcs that intersect each other at  " U "  . Join BU  . and extend it to V , we get $\angle$ VBC =45$°$

Step 5 :  Take radius of  2.8 cm and center "  B "  draw an arc that intersect our line BV at " W " . Join CW

Step 6 : Now take radius more than half of CW and cneter "  C " and " W "  draw two arc from both points on both side of line CW, and these arcs intersect at " X "  and " Y " .

Step 7 :  Join line XY and  that intersect line BV at "  A " .

This is our required triangle ABC .

Hope this information will clear your doubts about Construction .

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards