Question

$\Delta ABC\sim \Delta LMN$. In $\Delta ABC$, $AB=5.1$ cm, $\angle B={55}^o$, $\angle C={65}^o$ and $\frac{AC}{LN}=\frac{3}{5}$, then construct $\Delta LMN$.

Answer 1

Given, $\Delta ABC\sim \Delta LMN$,
$\frac{AB}{LM}=\frac{BC}{MN}=\frac{AC}{LN}=\frac{3}{5}$
$\Rightarrow \angle B=\angle M={55}^o$
$\Rightarrow \angle C=\angle N={65}^o$
$\Rightarrow \frac{AB}{LM}=\frac{3}{5}$
$\Rightarrow \frac{5.1}{LM}=\frac{3}{5}$
$\Rightarrow LM=\frac{5.1\times 5}{3}$
$\Rightarrow LM=1.7\times 5$
$\Rightarrow LM=8.5$ cm
In $\Delta LMN$, $LM=8.5$ cm, $\angle M={55}^o$, $\angle N={65}^o$
In $\Delta LMN$, we have
$\angle L+\angle M+\angle N={180}^o$
$\Rightarrow \angle L+{55}^o+{65}^o={180}^o$
$\Rightarrow \angle L+{120}^o={180}^o$
$\Rightarrow \angle L={180}^o-{120}^o$
$\Rightarrow \angle L={60}^o$

Now we can construct, $\Delta LMN$ using the following parameters:

$\angle L={60}^0,\angle N={65}^0,LM=8.5cm,\angle M={55}^0$