Question

If `Delta ABC` is drawn such that `m/_BAC=30^circ`, `AB=7`, `BC=4`. How many triangles can be drawn with this information?

Answer 1

Two

Explanation:

Steps construction

• Two line segments of 7 cm and 4 cm are drawn using ruler.
• A line segment `AK>7 cm` is drawn.
• From AK line segment AB=7cm is cut off using pencil compass.
• `/_BAL=30^@` is drawn using compass and ruler.
• An arc of radius 4 cm is drawn centering B . This arc intersects AL at C (two positions). Because the length of BC is greater than the perpendicular distance ( i.e.minimum distance) of B from AL.
  By trigonometry this perpendicular distance is `ABsin30^@=7xx1/2=3.5cm`

Joining B and C (two positions) we get two triangles..