Question

Draw a triangle with BC=7cm,angleB=45 degree,angleA=105 degree. then construct a triangle who sides are 4/3 time the corresponding sides of triangle ABC.

Answer 1

Sum of all side of triangle = 180°
∴ ∠A  + ∠B  + ∠C  = 180°
∠C = 180° - 150° = 30°
Steps of Construction:
Step I: BC = 7 cm is drawn.
Step II: At B, a ray is drawn making an angle of  45° with BC.
Step III: At C, a ray making an angle of 30° with  BC is drawn intersecting the previous ray at A. Thus, ∠A = 105°.
Step IV: A ray BX is drawn making an acute angle with BC opposite to vertex A.
Step V: 4 points B1 B2 B3 and B4 at equal distance is marked on BX.
Step VI: B3C is joined and B4C' is made parallel to B3C.
Step VII: C'A' is made parallel CA.
Thus, A'BC' is the required triangle.

Justification:

∠B = 45° (Common)
∠C = ∠C'
ΔAB'C' ~  ΔABC by AA similarity condition.
∴ BC/BC' = AB/A'B' = AC/A'C'
also,
BC/BC' = BB3/BB4 = 34
⇒ AB = 4/3 AB', BC = 4/3 BC' and AC = 4/3 A'C'