Question

Construct a ΔPQR with ∠Q = 60°, ∠R = 45° and the perpendicular from P to QR be 3.5 cm. Measure PQ.

Answer 1

Steps of construction:
1. Draw a line segment ST of any length.
2. From any point Y on ST, draw XY perpendicular to ST.
3. With Y as centre and radius 3.5 cm mark a point P on XY.
4. With P as centre, draw an arc cutting XY at L.
5. With L as centre and same radius, cut the arc at O and M. With M as centre and same radius cut the arc at N.
6. Draw PZ perpendicular to XY using M and N.
7. Bisect angles OPY and ZPY making 30° and 45° angles with PY respectively. (In triangle PQY, ∠PQY = 60°, ∠QYP = 90°; therefore ∠QPY = 30° and in  triangle PYR, ∠YRP = 45°, ∠RYP = 90°; therefore ∠YPR = 45°).
8. Join PQ and PR. PQR is the required triangle.
9. On measuring, PQ = 4.1 cm.