.A man is standing on the deck of a ship, which is 10m above water level. He observes the
angle of elevation of the top of a light house as 600 and the angle of depression of the base of
lighthouse as 300. Find the height of the light house.
Answers
Step-by-step explanation:
Let a man is standing on the Deck of a ship at point a such that AB = 10 m & let CE be the hill
Thus, AB = CD = 10 m
The top and bottom of a hill is E and C.
Given, the angle of depression of the base C of the hill observed from A is 30° and angle of elevation of the top of the hill observed from A is 60 °
Then ∠EAD= 60° &
∠CAE= ∠BCA= 30°. (Alternate ANGLES)
Let AD = BC = x m & DE= h m
In ∆ ADE
tan 60° = Perpendicular / base = DE/AD
√3= h/x [tan 60° = √3]
h = √3x……..(1)
In ∆ ABC
tan 30° = AB /BC
[ tan30° = 1/√3]
1/√3 = 10/x
x= 10√3 m.. …………..(2)
Substitute the value of x from equation (2) in equation (1), we have
h = √3x
h= √3× 10√3= 10 × 3= 30 m
h = 30 m
The height of the hill is CE= CD+ DE= 10 +30= 40 m
Hence, the height of the hill is 40 m & the Distance of the hill from the ship is 10√3 m.
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Answer:
Let AB=10m, cliff of a ship where man is standing
Let CE be the hill.
CD=AB=10m
In △ADE
tan60°=
x
h
3
x=h
x=
3
h
⟶(1)
In △ABC
tan30°=
x
10
3
1
=
x
10
x=10
3
⟶(2)
We have two equations (1) & (2), Multiplying them we get,
x
2
=10h
h=30m
∴CE=CD+DE=10+30=40m