in a triangle and we have ab=4 cm bc=5.6 cm and ca=7.6 cm write in ascending
Answers
1.Imagine/draw a horizontal line AB=6cm (given).
2. Imagine/draw another line drawn through BB , that is 60∘60∘ to ABAB . Somewhere on this line lies CC , such that AC=8cmAC=8cm .
The shortest distance between AA and the other line (60∘60∘ to ABAB ) is the perpendicular from AA to that line. Let the point where the perpendicular meets be XX . Now since AXAX is the shortest distance between AA and the line, any length longer than this could be drawn from AA to that line. Any line shorter than AXAX could not be drawn from AA to the 60∘60∘ line.
So, if we can show that AC>AXAC>AX , we know the triangle can be constructed.
In the right-angled triangle ABXABX (since AXAX is perpendicular to ABAB )
sin∠ABX=AXABsin∠ABX=AXAB
⇒AX=sin60∘×6⇒AX=sin60∘×6
⇒AX=0.866∘×6=5.196cm⇒AX=0.866∘×6=5.196cm (approximately)
Since AC=8cm>AXAC=8cm>AX , the triangle can be constructed.
To do so, follow steps 1 and 2 on paper, and then
3.Using a compass, draw a circle of radius 8cm8cm with AA as the center.
4.The intersection of the circle with the 60∘60∘ line is point CC .
5. Join ACAC to obtain triangle ABCABC .
Hope this helps!