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Purple Comet Problems
2003 Purple Comet Problems
24
Problem 24, Fall 2003 , MS and HS
Problem 24, Fall 2003 , MS and HS
Source:
June 23, 2011
trigonometry
Problem Statement
In
△
A
B
C
\triangle ABC
△
A
BC
,
∠
A
=
3
0
∘
\angle A = 30^{\circ}
∠
A
=
3
0
∘
and
A
B
=
A
C
=
16
AB = AC = 16
A
B
=
A
C
=
16
in. Let
D
D
D
lie on segment
B
C
BC
BC
such that
D
B
D
C
=
2
3
\frac{DB}{DC} = \frac23
D
C
D
B
=
3
2
. Let
E
E
E
and
F
F
F
be the orthogonal projections of
D
D
D
onto
A
B
AB
A
B
and
A
C
AC
A
C
, respectively. Find
D
E
+
D
F
DE + DF
D
E
+
D
F
in inches.
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