Construct a triangle $ABC$,in which $BC = 8 \, cm$,$\angle B = 75^{\circ}$ and $AB + AC = 15 \, cm$.
(N/A) Steps of construction:
$(1)$ Draw any ray $BX$. With centre $B$ and radius $8 \, cm$,draw an arc to intersect $BX$ at $C$.
$(2)$ At $B$,construct $\angle YBC$ with measure $75^{\circ}$.
$(3)$ With centre $B$ and radius $15 \, cm$,draw an arc to intersect $BY$ at $M$.
$(4)$ Draw line segment $MC$. Draw the perpendicular bisector of $MC$ to intersect $BM$ at $A$.
$(5)$ Draw line segment $AC$.
Then,$\Delta ABC$ is the required triangle.
$(1)$ Draw any ray $BX$. With centre $B$ and radius $8 \, cm$,draw an arc to intersect $BX$ at $C$.
$(2)$ At $B$,construct $\angle YBC$ with measure $75^{\circ}$.
$(3)$ With centre $B$ and radius $15 \, cm$,draw an arc to intersect $BY$ at $M$.
$(4)$ Draw line segment $MC$. Draw the perpendicular bisector of $MC$ to intersect $BM$ at $A$.
$(5)$ Draw line segment $AC$.
Then,$\Delta ABC$ is the required triangle.
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