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Geometry: Construction-Triangle when its base and vertical angle are given
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Geometric Construction: Triangle when its base and vertical angle are given

Steps:-
Step I: Draw a line segment equal to the base say BC of the triangle.
Step II: Below BC, make an angle CBP equal to the vertical angle of the given triangle.
Step III: Draw a line BE BP at the point B.
Step IV: Draw the right bisector of  BC meeting a line BE BP at O.
Step V: With O as the centre and OB as radius, draw a circle.
Step VI: Take any point A on the circumference of the circle on the same side on which O lies.
Step VII: Join AB and AC.
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Example: Construct a triangle with BC = 5.6 cm and vertex A such that mBAC = 60 . How many such triangles are possible?
Solution: Steps of Construction
Step I: Draw a line segment BC = 5.6 cm.
Step II: Below BC, make CBP = BAC = 60
Step III: Draw BE BP at the point B.
Step IV: Draw the right bisector QR of BC. Suppose QR meets BE at O.
Step V: With O as centre and OB as radius, draw a circle.
Step VI: Take any point A on the circumference of the circle on the same side on which O lies.
Step VII: Join AB and AC.

As any position on the arc BAC can be assumed, so there can be infinitely many such triangles.
 
   
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