Question

if triangle ABC is drawn such that m<BAC=30 Degree, AB=7, BC=4, How many triangles can be drawn with this information​

Answer 1

Answer:

• Two line segments of 7 cm and 4 cm are drawn using ruler.
• A line segment AK>7cm 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∘=7×12=3.5cm

Answer 2

Answer:

Steps for construction

1. Two line segments of 7 cm and 4 cm are drawn using ruler.

2. A line segment  A K > 7c m  is drawn.

3. From AK line segment AB=7cm is cut off using pencil compass.

4. ∠ B A L = 30 ° is drawn using compass and ruler.

5. 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  

A B  sin 30 ∘ = 7 × 1 2 = 3.5 c m

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