construct a triangle PQR in which angle Q = 45, angle R= 60, and the perpendicular from the vertex P to base QR = 5cm.

STEP I: Draw a line segment QR such that QR = 5 cm.
STEP II: Taking Q as a point, draw a line segment such that it makes an angle of 45$°$ with the line segment QR.
STEP III: Taking R as a point, draw a line segment such that it makes an angle of 60$°$ with the line segment QR.
STEP IV: Two line segments QP and RP both intersects at a point P such that <PQR = 45$°$ and <PRQ = 60$°$.
STEP V: Taking P as a point and draw a line PS$\perp$QR.
STEP VI: Therefore, a triangle PQR is formed with P as a vertex and PS$\perp$QR.