a solve A ABC with a=13, b=14 C=15.
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Using cosine rule, cosA=
2bc
b
2
+c
2
−a
2
=
2⋅14⋅15
14
2
+15
2
−13
2
=
2⋅14⋅15
14
2
+(15+13)(15−13)
=
2⋅14⋅15
14
2
+14⋅4
=
30
18
=
5
3
Now using double angle formula, cosA=1−2sin
2
2
A
⇒2sin
2
2
A
=1−cosA=1−
5
3
=
5
2
⇒sin
2
2
A
=
5
1
∴sin
2
A
=
5
1
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