Question

Construct a $∆\mathrm{ABC}$ such that $\mathrm{AB}=2.5\mathrm{cm}$, $\mathrm{BC}=6\mathrm{cm}$ and $\mathrm{AC}=6.5\mathrm{cm}$. Measure $\angle \mathrm{B}$.

Answer 1

First we draw a rough sketch

The steps for construction are given below:

Step 1: Construct a $∆\mathrm{ABC}$

Draw a line segment $\mathrm{AB}=2.5\mathrm{cm}$.

Considering $\mathrm{A}$ as a center and radius$=6.5\mathrm{cm}$, draw an arc.

Considering $\mathrm{B}$ as a center and radius$=6\mathrm{cm}$, draw another arc.

Let $\mathrm{C}$ be the point where the two arcs intersect. Join $\mathrm{AC}\mathrm{and}\mathrm{BC}$ and label the sides.

Thus, $∆\mathrm{ABC}$ obtained is the required triangle.

Step 2: Measuring $\angle \mathrm{B}$

Place the horizontal line of protractor along AB and then reading angle from where the side AC passes.

On measuring $\angle \mathrm{B}$, we see that

$\therefore \angle \mathrm{B}=90°$