Question

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are \frac { 4 }{ 3 } times the corresponding sides of ∆ABC.

Answer 1

Hey mate hope this helps you.

Answer 2

hey dear !!!



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here's your

SOLUTION ::


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'




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