Question

The points of three persons A, B and C are in collinear. Distance between the person A and C is
60/3 mts.
TOOL
1.Distance between the person C and the foot of the lighthouse is

a) 453 m
b) 45 m
c) 55 m
d) 553 m

2.If angle of elevation from C to the top of the light house is 45° then the height of the light house
is

a) 42 m
b) 53 m
c) 453 m
d) 45 m

3.If the angle of elevation from ship to the top of the light house is 30° then the distance between the
ship and the top of the light house is

a) 90 m
b) 80 m
c) 45 m
d) 100 m
4.If the length of the shadow of the light house is 4513 mts then the angle of elevation of the sun is

a) 60°
b) 45°
c) 30°
d) 90°

5.Time taken by person C to reach the lighthouse, if he swims at the speed of 3 m/sec is

a) 10 sec
b) 15 sec
c) 10 min
d) 15 min
​

Answer 1

Given : three persons A, B , C , are in collinear . Distance between the person A and C is 60√3mts

To Find : Distance between the person C and the foot of the lighthouse

Solution:

Let say  foot of the lighthouse is  is D

Tan 30° =  DB/AB

=> 1/√3  = DB/AB

=> AB = DB√3

Tan 60° =  DB/BC

=> √3  = DB/BC

=> BC = DB/√3

AB + BC = AC

=> DB√3 +  DB/√3 =  60√3

=>  3DB  + DB  = 180

=> DB = 45

AB = 45√3

BC =  45/√3 = 15√3

.Distance between the person C and the foot of the lighthouse is  = CD

Sin 60°  = DB/CD  => √3/2 = 45/CD

=> CD = 90/√3 = 30√3 m

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