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

M4maths Previous Puzzles

13 Sep 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 30° and 45° respectively. If the lighthouse is 169 m high, the distance between the two ships is:

OPtion

1) 460.72 m
2) 468.72 m
3) 463.72 m
4) 464.72 m
5) 461.72 m
6) 465.72 m
7) 467.72 m
8) 469.72 m
9) 462.72 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 = 169 m, Angle ACB = 30° and angle ADB = 45°.
AB/AC = tan 30° = 1/sq root(3)
=> AC = AB * sq root(3) = 169*3^(1/2)

AB/AD = tan 45° = 1
=> AD = AB = 169

CD = (AC + AD) = 169(3^(1/2) +1)
= 461.72

Correct Option: 5 Best Solution (7)

G.S.Kantharao   7 years AGO

Distance between the two Ships=x+y
Tan 45°=169/x -> x=169
Tan 30°=1/√3=169/y -> y=169√3 =292.72
X+y= 169 + 292.72=461.72
Hence the right option is 5👈.

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Santosh   7 years AGO

Tan30=169/x
X=292.716
Tan45=169/y
Y=169
X+Y=461.72

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mukund kumar   7 years AGO

p/b1=tan 30
p/b2= tan 45
b1=root 3 *169
b2= 1*169
b1+b2= (root3+1)169=461.7169 or in round 461.72

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swati jain   7 years AGO

If left ship will make 30° angle with the top of lighthouse then the distance between the ship and lighthouse will be 169√3
Right ship will make 45° angle with the top of lighthouse then the distance between this ship and lighthouse will be 169
Hence distance between both ships =169+169√3=461.72

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KRISHAN KANT VASHISHTH   7 years AGO

Angles of elevations are: 30 and 45
Height of LightHouse =169
Distance = 169(1+sqrt(3)) // Sum of angle of elevations as they represent the base one and base two between ship one and second ship to the lighthouse.
= 169*2.732 = 461.72

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sanjeet kumar   7 years AGO

ab=height
ab=root 3*169(angle of 30 degree)
ab/ad=1(angle of 45 degree=tan45=1)
ab=ad=169
169(root3+1)=461.72

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Varun   7 years AGO

It is 169/tan30 + 169/tan45 =461.716

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