22 m
18
7 m
A
B
C
D
?
E
Q. Two poles of height 18 metres and 7 metres are erected
on the ground. A wire of length 22 metres is tied to the
top of the poles. Find angle made by wire with the horizontal.
Horizontal line can be drawn from point ‘A’
as well as ‘C’
Consider CE ⊥ AB
AE = 11 m
In right angled Δ AEC,
sin C =
sin C =
sin C =
But, sin 30o =
sin C = sin 30o
∠C = 30o
The angle made by wire with the horizontal is 30o
AE
AC
11
22
1
2
1
2
22 m
18m
7 m
A
B
C
D
?
E
Sol.
Q. Two poles of height 18 metres and
7 metres are erected on the ground.
A wire of length 22 metres is tied to
the top of the poles. Find angle made
by wire with the horizontal.
Observe ∠ACE
For ∠ACE
Opposite side →
Hypotenuse →
AE
AC
Ratio of opposite side and Hypotenuse reminds us of _________
‘sin’
Consider ΔAEC
1
2
sin 30º =
But we know that,
∴
∴
Opposite
side
AB and CD represent the heights of two poles.
AC represents the length of wire.
∠ACE is the angle made by the wire with the
horizontal.
□EBDC is a rectangle
CD = EB = 7m
AE +
EB
=
AB
AE +
7
=
18
∴
∴
Hypotenuse
Observe □EBDC
Observe AB
11m
7 m
∴