Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
In any triangle
A
B
C
ABC
A
B
C
,
a
2
sin
(
B
−
C
)
sin
B
+
sin
C
+
b
2
sin
(
C
−
A
)
sin
C
+
sin
A
+
c
2
sin
(
A
−
B
)
sin
A
+
sin
B
=
\frac{a^2 \sin(B-C)}{\sin B + \sin C} + \frac{b^2 \sin(C-A)}{\sin C + \sin A} + \frac{c^2 \sin(A-B)}{\sin A + \sin B} =
s
i
n
B
+
s
i
n
C
a
2
s
i
n
(
B
−
C
)
+
s
i
n
C
+
s
i
n
A
b
2
s
i
n
(
C
−
A
)
+
s
i
n
A
+
s
i
n
B
c
2
s
i
n
(
A
−
B
)
=
a.
a
+
b
+
c
a + b + c
a
+
b
+
c
b.
a
+
b
−
c
a + b - c
a
+
b
−
c
c.
a
−
b
+
c
a - b + c
a
−
b
+
c
d. 0
Browse the problem library