Construct a $\vartriangle ABC$ in which $AB\ =\ 6\ cm$, $\angle A\ =\ 30^{o}$ and $\angle B\ =\ 60^{o}$, Construct another $\vartriangle AB’C’$ similar to $\vartriangle ABC$ with base $ AB’\ =\ 8\ cm$.
Given: A $\vartriangle ABC$ in which $AB\ =\ 6\ cm$, $\angle A\ =\ 30^{o}$ and $\angle B\ =\ 60^{o}$.
To do: To construct $\vartriangle ABC$ and also to construct another $\vartriangle AB’C’$ similar to $\vartriangle ABC$ with base $ AB’\ =\ 8\ cm$.
Solution:
Steps of construction:
$( i)$. Draw a line $AB$ of length $6\ cm$.
$( ii)$. Make an angle of $30^o$ at $A$ and extend the line from $A$ making this angle.
$( iii)$. Make an angle of $60^o$ at $B$ and extend the line from $B$ making this angle till it meets the line from step $2$ at point $C$.
Hence, we got the $\vartriangle ABC$
Steps of construction of $\vartriangle AB'C'$:
$( iv)$. Extend the line $AB$ to $B′$, such that $AB′=8\ cm$.
$( v)$. Make an angle of $60^o$ at $B′$ and extend the line from $B′$ making this angle till it meets the line from step $2$ at point $C'$.
Hence, we got the $\vartriangle AB'C′$.
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