Question

Construct a triangle $ABC$ in which $BC=7cm,\angle B={75}^o$ and $AB+AC=13cm$.

Answer 1

R.E.F. Image.

Given,

to construct a $\Delta ABC$ where

$BC=7cm,\angle B={75}^{\circ }$ & $AB+AC=13cm.$

construction steps :-

(i) Draw a line segment BC = 7 cm as a base.

(ii) Now mark $\angle B={75}^{\circ }$ and extend it till x.

(iii) Now, by taking radius 13 cm draw an arc from 'B' on the line of angle just projected.

(iv) Now mark it as 'D', & join C to D.

(v) Draw ${\perp }^{lar}$ bisectors for DC and mark them as P & Q.

(vi) Now extend a line from 'B' to the ${\perp }^{lar}$ bisector that cuts on C & D line.

(vii) Now mark that point as 'A'.

(viii) Thus, required $\Delta ABC$ has been formed.

(ix) Now, try taking exactly 1/2 of the angle and mark an arc on B.

Conclusion :-

$\therefore$ The required $\Delta ABC$ will BC = 7 cm,

$\angle B={45}^{\circ }$ & AB + AC = 13 cm is constructed.