30o
B
75 m
45o
30o
A
D
C
45o
X
∠XBC and ∠BCA are what type of angles?
Alternate angles
What can we say about these two angles ?
They are equal
∠XBD and ∠BDA are what type of angles?
Alternate angles
What can we say about these two angles ?
They are equal
Q. As observed from the top of a 75 m high lighthouse from the
sea-level, the angles of depression of two ships are 30° and 45°.
If one ship is exactly behind the other on the same side of the lighthouse,
find the distance between the two ships.
Observer
Observe
∠XBC and ∠BCA
Observe
∠XBD and ∠BDA
line of sight
line of sight
Horizontal line
?
Q. As observed from the top of a 75 m high
lighthouse from the sea-level, the angles
of depression of two ships are 30° and 45°.
If one ship is exactly behind the other on
the same side of the lighthouse,
find the distance between the two ships.
Sol.
Height of light house (AB) = 75 m
AD is the distance of one ship from
the foot of light house (AB)
Let the distance between
two ships (DC) be ‘x’ m
In right ΔBAD,
tan 45º
=
AB
AD
∴
1
=
75
AD
…(i)
∴
AD
=
75m
A
D
C
B
75 m
X
45º
30º
30º
45º
x
Opposite
side
Adjacent side
tan 45o =
?
1
Observe ∠ADB
For ∠ADB
Opposite side →
Adjacent side →
AB
AD
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
Consider ΔBAD
75m
In right ΔBAC,
tan 30º
=
AB
AC
∴
1
=
75
x + 75
∴
x + 75
=
75
∴
x
=
75
– 75
∴
x
=
75(
– 1)
∴
Distance between the two ships is 54.75 m
∴
x
=
75(
1.73 – 1)
∴
x
=
75 ×
∴
x
=
54.75
Q. As observed from the top of a 75 m high
lighthouse from the sea-level, the angles
of depression of two ships are 30° and 45°.
If one ship is exactly behind the other on
the same side of the lighthouse,
find the distance between the two ships.
Sol.
A
D
C
B
X
45º
30º
30º
45º
x
75m
75 m
(x + 75)m
Opposite
side
Adjacent side
For ∠ACB
Opposite side →
Adjacent side →
AB
AC
tan 30o =
?
1
Ratio of opposite side and Adjacent side reminds us of _________
‘tan’
Observe ∠C
0.73