what is the smallest angle of the triangle whose sides are 6+root 12,root 48,root 24
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Step-by-step explanation:
Since the smallest angle is opposite to the smallest side, we can use the law of cosines.
a
2
=b
2
+c
2
−2bccosA
On simplification:cosA=
2cb
b
2
+c
2
−a
2
Substituting the values we have
cosA=
2(6+2
3
)(4
3
)
(6+2
3
)
2
+(4
3
)
2
−(2
6
)
2
=
2(6+2
3
)(4
3
)
48+24
3
+48−24
On taking numerator in terms of 2,
=
(6+2
3
)(4
3
)
36+12
3
On taking numerator in terms of 2,=
(6+2
3
)(4
3
)
36+12
3
And finally cosA=
2
3
=cos30
∘
=cos
12
π
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