Answer:
Its typically helpful to start with a drawing. Here is
A
B
C
D
as given by the problem.
Geogebra
Geogebra
We are looking for the length of the shorter diagonal, which is segment
B
D
. This segment forms a triangle with the two known sides. Since we know two sides and the angel connecting them, we can use the law of cosines to solve for the unknown segment.
http://mathworld.wolfram.com/LawofCosines.html
http://mathworld.wolfram.com/LawofCosines.html
The law of cosines tells us that
c
2
=
a
2
+
b
2
−
2
a
b
cos
(
C
)
for the triangle labeled above. If we choose our two known sides for
a
and
b
and our known angle for
C
, we can solve for the length of the diagonal,
c
.
c
2
=
14
2
+
8
2
−
2
(
14
)
(
8
)
cos
(
60
o
)
≈
12.17
Step-by-step explanation:
sorry about the last answer i thought i was on another question
