M4maths Previous Puzzles

09 Aug 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 30° respectively. If the lighthouse is 144 m high, the distance between the two ships is:

OPtion

1) 312.55 m
2) 322.55 m
3) 362.55 m
4) 302.55 m
5) 342.55 m
6) 352.55 m
7) 332.55 m
8) 372.55 m
9) 382.55 m
10)None of these

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 = 144 m, Angle ACB = 60° and angle ADB = 30°.
AB/AC = tan 60° = sq root(3)
=> AC = AB / sq root(3) = 144/3^(1/2) = 48*3^(1/2)

AB/AD = tan 30° = 1/sq root(3)
=> AD = AB*sq root(3) = 144*3^(1/2)

CD = (AC + AD) = 3^(1/2) (48+144)
= 192*3^(1/2)
= 332.55

Correct Option: 7 Best Solution (22)

SAYAN CHATTERJEE   7 years AGO

Distance between two ships is 144*(1/tan60+a1tan30)
= 332.55
Option 7.

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Mukund Manohar   7 years AGO

Required Distance = 144/tan 60 + 144*tan 30
= 144/sq.root(3) + 144*sq.root(3)
= 332.55 m

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shreya   7 years AGO

144/x = tan 30
144/y =tan 60
x+y= 144√3 + (144/√3) =332.55

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G.S.Kantharao   7 years AGO

Angle of elevations are 60,30 degrees
Height of the light house =144 mts.
Tan 60= 144/x=
144/x =√3
X=144/√3
Tan 30 =144/y=1/√3
Y=144√3
Distance between the ship's is =x + y
X+y=144/√3+144√3=(144+144*3)/√3=576/√3=332.5 mts.
Hence the right option is 7 👈.

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mandeep   7 years AGO

tan 60=144/x
tan 30=144/y
find x and y and then add both to get 332.55

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Divakar   7 years AGO

easy
tan60 = 144/x
x= 144/3^1/2. similarily, tan30 = 144/y
y = 144* 3^1/2
x+Y = 332.55

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Ravi   7 years AGO

let AB=144 so angle Angle ACB=60° AND ANGLE ADB=30° SO AB/AC=tan60° and AB/AD=tan30° so after solving we will get AC and AD value after adding we get 332.55m

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tumati koushik   7 years AGO

x1=144/tan 60 ,x2 =144/tan30
x= x1+x2=144(4/sqrt3)
x=332.5538

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Madhuvani v   7 years AGO

Let AB be the lighthouse and C and D be the positions of the ships.
AB=144m,∠ACB=60,∠ADB=30∘
AB/AC=tan60=√3
AC=144/√3
AB/AD= tan30 =1/√3
AD=144√3
CD=AC+AD=( 144/√3+144√3)=144(1/√3+√3)=332.55 m
ans=7

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sangita kundu   7 years AGO

let the distance between the lighthouse and one ship is x1 and another one is x2 and the angle is 60°and 30°.
sin30°= x1/144 and sin60°=x2/144.
from these two equation we get the values of xand x2.then we add these values.i.e. the required answer

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Vignesh   7 years AGO

Angle of elevation from lighthouse for first boat 60° and for second 30°.
Height = 144 m.

For first boat:


cos 60° = 144/ hyp
Hyp= 288
Sin 60° = X / 288
X = 249.4 m

For second boat :

Cos 30° = 144/ hyp
Hyp= 166.2
Sin 30° = y / 166.2
Y = 83.138 m

Distance = x + y
= 332.55 m

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umend   7 years AGO

Let ship be at a distance of x and y from lighthouse
Then tan60=144/x
tan30=144/y
We get x=83.14. y=249.41
Distance between two ships=x+y=83.14+249.41
=332.55
Ans:332.55

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Bodla Anupriya   7 years AGO

144(tan30+tan60)=144(1/√3 +√3 )
=332.55

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palak Jain   7 years AGO

angle of elevation of first ship=60 degree
So,tan 60=p/b1 =144/b1
so,b1=144/1.732
tan 30=p/b2
so,b2=144*1.732
b1+b2=332.55 m

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Himaja   7 years AGO

let a triangle is bcd .there is lighthouse of height 144m i.e ab.ab/ac=tan60,ab/ad=tan30,cd=ac+ad.finally ac=144/1.73 and ad=144*1.73.so,cd=332.55m

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Sethu Bargavi M   7 years AGO

tan 60 = 144/B
Ship1 distance from light house = 144/1.732 (sq.root of 3) = 83.14
tan 30 = 144/B
Ship2 distance from light house = 144*1.732 = 249.40

Add both 332.54

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kanimozhi kalimuthu   7 years AGO

consider distance between ship 1 and ship 2 be x,y respectively
tan 60=opp/adj=144/x
x=83.13
tan 30=144/y
y=249.41
distance=(x+y)=83.13+249.41=332.55m

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Sahil Mehta   7 years AGO

tan 60=144/base
base=√3*144
base=249.12 m
tan30=144/base2
base2=83.2 m
the total distance will be =base 1 +base2
249.12+83.2 =332.55 m

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AYAN PAUL   7 years AGO

From the question we can write the distance between a ship and the lighthouse is = 144*1.732 = 249.408
and the distance from the lighthouse to another ship is 144/1.732 = 83.14
Now combining these two distance we can write the total distance between two ships will be = 249.408 + 83.14 = 332.55 m (approximately)

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prasanna   7 years AGO

Let's take The distance between lighthouse and ship1 is x and distance between lighthouse and ship2 is d-x than by giving that angles from lighthouse to ships are 30 and 60
By solving trigonometric equations we get the distance between 2 ships is 332.55m

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ANANDA PRIYA T.R   7 years AGO

On one end of the light house the
Distance is (144/tan 60)=83.138
On the other side of the light house the
Distance is (144 /tan 30) =249.41
83.138 +249.41 =332.548

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shashank kumar singh   7 years AGO

Let base be x.
tan(30)=144
x=144×√3
tan(60)=144
x=144÷√3
By adding both the x we get 332.548

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