1.

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 ​

Answer»

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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