Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top

M4maths Previous Puzzles

16 Mar 2017 Distance

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 60° and 45° respectively. If the lighthouse is 123 m high, the distance between the two ships is:

OPtion

1) 146.67 m
2) 197.67 m
3) 153.9 m
4) 199.3 m
5) 171.3 m
6) 193.1 m
7) 182.5 m
8) 185.2 m
9) 190.4 m
10)194.0 m

Solution

Let AB be the lighthouse where A is the bottom point of light house and C and D be the positions of the ships.
Then, AB = 123 m, Angle ACB = 60° and angle ADB = 45°.
AB/AC = tan 60° = sq root(3) AC = AB / sq root(3) = 123/3^(1/2) = 41*3^(1/2)
AB/AD = tan 45° = 1 AD = AB = 123 m.
CD = (AC + AD) = 41*3^(1/2) + 123
= 41(3^1/2 + 3)
= 194 m
Option 10)

Correct Option: 10 Best Solution (12)

G.S.Kantharao   7 years AGO

Hight of lighthouse = 123mts.
Angles of elevation =60°, 45° respectively.
Let the distances of the ships are x,y respectively from the lighthouse
Then the distance between the ships = x + y
Tan 60° = 123/x =√3
x = 123/√3 = 41√3 = 41*1.732 = 71.014mts.
Tan45° = 123/y =1
y = 123mts.
Now x +y= (123+71.014)mts.=194.014mts.= 194mts. (approximately)
Hence the right option is 10.

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Harsh Poddar   7 years AGO

Distance of first ship from lighthouse is 123/tan45°=123
Distance of second ship from lighthouse is 123/tan60°=71
Distance between two ships is 123+71=194
Option 10

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Bupathikavya   7 years AGO

tan 45 = 123/x1 ...1= 123/x1....x1 = 123
tan 60 = 123/x2....root3 = 123/x2.....x2=123/root3
x1+X2 = 123+123/root3 = 194.0

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Hitesh Kumar Tiwari   7 years AGO

Let the height of the light house is AB , and the sides are J and K
so AJB =60
and AKB =30

so JK = 123/tan45 + 123/tan60
= 123 + 71.01
= 194.0M

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DIVYANSHU SHEKHAR   7 years AGO

tan 60=123/x
=>x=123/1.732=71.01m
tan 45=123/y
=>y=123/1=123m
distance b/w ships=x+y=194.01m

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Payal   7 years AGO

let distance between lighthouse be a and b respectively
then a= height_of_lighthouse/tan(60)
=123/1.732 = 71.01 m
b=height_of_lighthouse/tan(45)
= 123/1 = 123 m
distance between ships = a+b =71.01+ 123 =194 m

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Malsoor Bhukya   7 years AGO

tan60=AB/PB
1.73=123/x--> x=71.09
tan45=AB/BQ
1=123/y--> y=123
PQ=PB+BQ--->
PB=x+y--> 123+71.09=194.0m

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sagar wani   7 years AGO

two ships form a base angle of 45deg and 60 deg respectively. it forms two triangle with a common side(light house) 123m in height. the ship whcih can see the lijght house at an angle of 45deg form an isosceles triangle and hence the base distance from light house would be the height of light house i.e 123m. now the other ship forms the base angle of 60 deg. now hypotenuse can be found by sin 60 as we know the angle and height of light house. and once we find the hypotenuse we can find the base with Pythagoras thm.

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Devendra Marghade   7 years AGO

Let the ship making angle of 60 degree is at distance x m. and the ship making angle of 45 degree is at y m. from the lighthouse, then
tan60 = 123/x => x=123/sqrt(3)=71.016 and
tan45 = 123/y => y=123
Distance between the two ships=x+y =71.016+123= 194.01
Option 10)

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Azim Uddin Siddiqui   7 years AGO

sin60°=root 3/2:
root3/2= 123/h1
h1=123*2/root3
cos60°=1/2
so 1/2=distance of 1st ship from the base of tower(x)/h1
substituting values v get
1/2=root3* x/2*123; simplifying v get
x=123/root3;
x=71.014;
since in second case angle of elevation is 45°, it means triangle formed is an isocles triangle so the two sides will b equal i.e. the distance of the second ship from the base of tower is (y)= 123
addin x+ y v get distance between the ships, i.e. 123+71.014= 194.014

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somveer   7 years AGO

We have
Angle= 60° and 45°
length =123m
Now we are creating a rectangular ABC
Height AD=123m
Angle ACB=45° & ABC=60°
AD/DC=tan45°
123/DC =1
DC =123m
Hence
AD/DB= tan60°
123/DB = √3
so, DB= 71.016m
now BC =CD+DB
BC =123+71.016=194.016m
so, two ships distance was 194.0m.

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Naga   7 years AGO

The two ships are on the opposite side
distance of the first ship from the light house
x = 123/tan60
=71.014
distance of the second ship from the light house
y=123/tan45
=123
The two ships are on other sides of the light house.
so the distance between the two ships is
123+71 = 194

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