Construct $△$ RST such that RT = 5.7 cm , $∠$ RST = 55 $°$ ,SD $⊥$ RT and SD = 3.4 cm.

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Solution

Steps of construction:
(i) Draw a line segment RT = 5.7 cm.
(ii) Through R, draw RY such that $∠$ TRY= 55 $°$ .
(iii) Draw RX $⊥$ RY.
(iv) Draw the perpendicular bisector of RT intersecting RX at O and RT at H.
(v) With O as the centre and OR as the radius, draw a circle.
(vi) The major arc RWT of the circle contains the vertical 55 $°$ .
(vii) With H as the centre cut off HP = 3.4 cm.
(viii) Draw a line SS' parallel to RT passing through P.
(ix) With S as the centre, draw a line parallel to PH intersecting RT at D.
(x) Join ST and SD.

Thus, $△$ RST or $△$ RS'T is the required triangle.

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Construct △RST such that RT = 5.7 cm , ∠RST = 55° ,SD⊥RT and SD = 3.4 cm.

Construct $△$ RST such that RT = 5.7 cm , $∠$ RST = 55 $°$ ,SD $⊥$ RT and SD = 3.4 cm.