Answer:
52 feet
Step-by-step explanation:
From the problem, we are given that the angle of elevation as 37 degrees and you are 123 feet from the base of the building. How long a zipline is needed if you are 6 feet tall?
Let us consider a triangle
A
B
C
in which we have a line from
A
to
B
C
with a point named
D
Given that
D
C
=
152
foot and
∠
D
A
B
=
28
∘
,
∠
C
A
B
=
39
∘
.
Now we have to find the height of the flagpole
A
B
So, from the applying the tangent formula we get,
tan
(
39
)
=
B
C
A
B
A
B
=
(
B
D
+
D
C
)
0.809
A
B
=
(
100
+
D
C
)
(
0.809
)
(
equation 2
)
tan
(
28
)
=
B
D
A
B
A
B
=
100
(
0.531
)
(
equation 1
)
Now, we have two expressions for AB so we we equate both equations 1 and 2,
(
100
+
D
C
)
(
0.809
)
=
100
(
0.531
)
D
C
=
100
(
1.523
−
1
)
D
C
=
100
(
0.523
)
D
C
=
523
Therefore, the length of the zipline is
52
feet.
