side lengths bc = a , ca = b , ab = c of a triangle abc satisfy a³+b³+c³/a+b+c =c² find angle bca in degree please give correct answer its very urgent
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Answer:
Correct option is
B
45
In △ABC,
Sides a,b,c
⇒ c
2
=2ab [ given ] ----- ( 1 )
⇒ a+c
2
=3b
2
[ Given ] ----- ( 2 )
⇒ a
2
+2ab=3b
2
[ From ( 1 ) ]
⇒ a
2
+2ab+b
2
=4b
2
[ Adding b
2
on both sides ]
⇒ (a+b)
2
=4b
2
⇒ a+b=±2b
Since, a,b,c are sides then they are always positive.
∴ a+b=2b
∴ a=b
Substitute a=b in equation ( 1 ) we get,
⇒ c
2
=2a
2
⇒ c=
2
a
We can see,
c
2
=a
2
+b
2
c
2
=a
2
+a
2
c=
2
a
∴ We can see ABC is right angled triangle and c is the hypotenuse.
⇒ ∠C=90
o
⇒ ∠A+∠B=90
o
⇒ ∠A+∠A=90
o
[ Base angles of an equal sides also an equal ]
⇒ 2∠A=90
o
∴ ∠A=45
o
∴ ∠BAC=45
o
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