Question
Construct a triangle using the given data: $BC = 6.0\ cm, \angle B = 60^\circ $ and $\angle C = 45^\circ $
✓
Answer
$BC = 6.0\ cm, \angle B = 60^\circ $ and $\angle C = 45^\circ $
Steps of Construction:
$1$. Draw a line segment $BC = 6\ cm.$
$2$. With $B$ as centre, draw an arc meeting $BC$ at $M.$
$3$. With M as centre and same radius, cut the arc at $N.$
$4$. Produce $BN$ to $BX. BX$ makes an angle of $60^\circ $ with $BC.$
$5$. With $C$ as centre, draw an arc meeting $BC$ at $P.$
$6$. With $P$ as centre and same radius, cut the arc at $Q$ and with $Q$ as centre and same radius, cut the arc at $R.$
$7.$ With $Q$ and $R$ as centre, cut arcs and draw $CY$ perpendicular to $BC.$
$8$. Bisect $\angle YCB$. Let $CZ$ be the bisector. $CZ$ makes an angle of $45^\circ $ with $BC.$
$9$. Mark the point as $A$, where $CZ$ and $BX$ cut each other.
Thus, $\text{ABC}$ is the required triangle.
Steps of Construction:
$1$. Draw a line segment $BC = 6\ cm.$
$2$. With $B$ as centre, draw an arc meeting $BC$ at $M.$
$3$. With M as centre and same radius, cut the arc at $N.$
$4$. Produce $BN$ to $BX. BX$ makes an angle of $60^\circ $ with $BC.$
$5$. With $C$ as centre, draw an arc meeting $BC$ at $P.$
$6$. With $P$ as centre and same radius, cut the arc at $Q$ and with $Q$ as centre and same radius, cut the arc at $R.$
$7.$ With $Q$ and $R$ as centre, cut arcs and draw $CY$ perpendicular to $BC.$
$8$. Bisect $\angle YCB$. Let $CZ$ be the bisector. $CZ$ makes an angle of $45^\circ $ with $BC.$
$9$. Mark the point as $A$, where $CZ$ and $BX$ cut each other.
Thus, $\text{ABC}$ is the required triangle.
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