Question

Construct a triangle $ABC$ in which base $AB=5cm,\angle A={30}^{\circ }$ and $AC-BC=2.5cm$

Answer 1

Steps of construction
$1$. Draw a line segment $AB$ of length $5cm$.
$2$. Draw another line segment $AX$, sufficiently large, such that $\angle BAX={30}^{\circ }$.
$3$. From the segment $AX$, cut off line segment $AD=2.5cm$, which is equal to $(AC-BC)$.

$4$ Join $BD$
$5$. Draw the perpendicular bisector of $BD$ and let it cut $AX$ at $C$.
$6$. Join $BC$.
Then $ABC$ is the required triangle.