Question

Construct a triangle whose sides are $3.6\mathrm{cm}$, $3.0\mathrm{cm}$ and $4.8\mathrm{cm}$. Bisect the smallest angle and measure each part.

Answer 1

Step 1: Constructing the triangle

Draw a line $\mathrm{AB}=$ $4.8\mathrm{cm}$.

Now, assume a radius of $3.6\mathrm{cm}$ and centre $\mathrm{A}$ to draw an arc. And consider the radius of $3.0\mathrm{cm}$ and centre $\mathrm{B}$, draw an arc that intersects our previous arc at $\mathrm{C}$.

Join $\mathrm{CA}$ and $\mathrm{CB}$, we get the required triangle $\mathrm{ABC}$.

Step 2: Bisecting the smallest angle

$\angle \mathrm{A}$ is the smallest angles because the angle in front of the smallest side is the smallest. So, we will bisect $\angle \mathrm{A}$.

With $\mathrm{A}$ as center, draw an arc which cuts $\mathrm{AC}$ and $\mathrm{AB}$ at point $\mathrm{F},\mathrm{E}$ respectively.

With $\mathrm{E}$ and $\mathrm{F}$ as center, draw arcs which intersect at $\mathrm{G}$.

Draw line $AG$ which passes through $\mathrm{D}$, where $\mathrm{D}$ is a point on $BC$.

Step 3: Measuring each part

Now , we can easily measure each other angle with the help of protractor.

We get, $\angle \mathrm{A}=40°,\angle \mathrm{B}=50°,\angle \mathrm{C}=90°$