In each of the following cases, give reason to show that the construction of Delta ABC is not possible. (i) AB=6 cm, angleA=45^(°) and (BC+AC)=5.8 cm. (ii) AB=5 cm, BC=4 cm and AC=9 cm. (iii) AB=5.4 cm, angleB=60^(°) and (BC-AC)=6 cm. (iv) BC=4 cm, angleA=80^(°), angleB=50^(°) and angleC=60^(°).
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In each of the following cases,given reasons to show that the construction of Δ ABC is not possible : iAB =6 cm , ∠ A = 40∘ and BC + AC =5.58 cmii AB =7 cm , ∠ A =50∘ and BC AC =8 cmiii BC =5 cm , ∠ B =80∘, ∠ C =50∘, and ∠ A =60∘iv AB =4 cm , BC =3 cm, and AC =7 cm.
Question
In each of the following cases,given reasons to show that the construction of
Δ
A
B
C
i
s
n
o
t
p
o
s
s
i
b
l
e
:
(
i
)
A
B
=
6
c
m
,
∠
A
=
40
∘
a
n
d
(
B
C
+
A
C
)
=
5.58
c
m
(
i
i
)
A
B
=
7
c
m
,
∠
A
=
50
∘
a
n
d
(
B
C
−
A
C
)
=
8
c
m
(
i
i
i
)
B
C
=
5
c
m
,
∠
B
=
80
∘
,
∠
C
=
50
∘
,
a
n
d
∠
A
=
60
∘
(
i
v
)
A
B
=
4
c
m
,
B
C
=
3
c
m
,
a
n
d
A
C
=
7
c
m
.
Solution
ANSWER:
(i) AB = 6 cm,
∠
A
= 40° and ( BC + AC ) = 5.8 cm.
Here BC + AC is not greater than AB so, this triangle is not possible.
(ii) AB = 7 cm,
∠
A
= 50° and ( BC – AC ) = 8 cm.
Here BC – AC is not less than AB so this triangle is not possible.
(iii) BC = 5 cm,
∠
B
= 80°,
∠
C
= 50° and
∠
A
= 60°.
Sum of the angles of the given triangle is not equal to 180° so, given triangle is not possible.
(iv) AB = 4 cm, BC = 3 cm and AC = 7 cm.
Sum of two sides of this triangle not greater than the third side so given triangle not possible.