M4maths Previous Puzzles

09 Jan 2018 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 30° and 30° respectively. If the lighthouse is 69 m high, the distance between the two ships is:

OPtion

1) 231.02 m
2) 232.02 m
3) 233.02 m
4) 234.02 m
5) 235.02 m
6) 236.02 m
7) 237.02 m
8) 238.02 m
9) 239.02 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 = 69 m, Angle ACB = 30° and angle ADB = 30°.
AB/AC = tan 30° = 1/3^(1/2)
=> AC = AB * 3^(1/2) = 69*3^(1/2)

AB/AD = tan 30° = 1/3^(1/2)
=> AD = AB*3^(1/2) = 69*3^(1/2)

CD = (AC + AD) = 69*3^(1/2) + 69*3^(1/2)
= 239.02

Option 9)

Correct Option: 9 Best Solution (14)

Dr.Dipin Singh   6 years AGO

Distance between ships = 2*69*Sqrt 3= 239.02 mtrs

Like? Yes (2) | No   

Harshita   6 years AGO

tan 30 deg= 69/distance of lighthouse from ship1
distance = 69 * root 3 m
now distance between two ships = 2*69*root 3
ans = 239.02 m

Like? Yes (2) | No   

Karan   6 years AGO

Distance of each ship from lighthouse = 69 tan 30 deg = 69* ( Sqrt 3) metres
Distance between two ships = 2*69*(sqrt3) = 239.02 m

Like? Yes (1) | No   

Swati   6 years AGO

Distance of one ship from the lighthouse=
(tan30) *69=119.508
So,distance between two ships=2*119.508=239.02

Like? Yes (1) | No   

SOPHIA   6 years AGO

tan 30 = height of light house/distance of first ship
tan 30=69/x
x=119.51
both ships have same angle of inclination
so,total distance=2x=239.02m

Like? Yes (1) | No   

AYAN PAUL   6 years AGO

Let the distance between the first ship to Lighthouse is X m.
So we can write 69/X = tan 30 Solving this we will get X = 119.51 m
Similarly we can find the distance between 2nd ship and lighthouse by solving 69/Y = tan 30 where Y is the distance of 2nd ship from Lighthouse
So Y will be 119.51 m
So X+Y will be 119.51+119.51 = 239.02 m

Like? Yes | No (1)  

Varun   6 years AGO

tan of angle = Length of opposite side to the angle/ Length of adjacent side
tan 30 = 69/distance between ship and bottom of light house
=> Distance of ship to bottom of light house = 119.51
So, distance between the 2 boats = 119.51*2 = 239.02
= Option 9)

Like? Yes | No (1)  

Devendra Marghade   6 years AGO

Let distancfrom one side making angle 30 degree upto the lighthouse be x m. and from other side be y m.
tan30=Height/Distance
=> (Sqrt3)/3=69/x and (Sqrt3)/3=69/y
=> x=207/(Sqrt3) and y=207/(Sqrt3)
So total distance=x+y=2*207/(Sqrt3)=239.02 m.
Option 9)

Like? Yes | No (1)  

G.S.Kantharao   6 years AGO

Tan 30°=69/x=1/√3=>x=69√3
Distance between two ships =138√3=239.02m
Hence my option is 9👈

Like? Yes | No (1)  

ARINJOY GHOSH   6 years AGO

let the distance between two ships be 2d.
according to question , tan 30= 69/d
so, d= 69*sqrt(3)
so,2d=2*69*sqrt(3)=239.02
ans : option-(9)

Like? Yes | No (1)  

Mukund Manohar   6 years AGO

Required Distance = (69/tan 30) + (69/tan 30) = 239.02 m

Like? Yes | No (1)  

Poulomi Maji   6 years AGO

The height of the lighthouse =AB=69 m
Two ships are sailing in the sea on the two side of the lighthouse and the angle of elevation of the top of the lighthouse from the ships are 30° & 30° respectively .

Let the distance between a ship and the lighthouse be BC

tan30°=AB/BC
=> BC=AB/tan30°
=>BC=69/tan30°
=> BC= 119.511m

The distance between another ship and the lighthouse =119.511

So the distance between two ships=119.511*2
=239.02m

Like? Yes | No (1)  

shubham sutar   6 years AGO

h=69m
horizontal distance between ship and lighthouse=69*cot(30)
so,dist between ship=2*69*cot(30)
=239.02

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Chanchal Dutta   6 years AGO

h/l=tan30
=>l=69/tan30
=>l=119.5115

2l=239.02

Like? Yes | No (1)