*** & varnematics (Class 10)
31. Two lamp-posts are of equal height. A boy measured the angle of elevation of the top of
each lamp-post from the mid-point of the line joining the feet of the lamp-posts as 30°.
After walking 15 m towards one of them, he measured the angle of elevation of its top at
the point where he stands, as 60°. Find the height of each lamp-post and the distance
between them
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Height of Lamp posts = 15√3 / 2 m & distance between them = 45 m
Step-by-step explanation:
Let say Height of Pole = H m
Distance between Poles = 2D m
Distance of Mid point = 2D/2 = D m
Tan 30 = H/D
=> 1/√3 = H/D
=> D = H√3
=> H = D/√3
After walking 15 toward lamp post
Tan 60 = H/(D - 15)
=> √3 = H/(D - 15)
=> D - 15 = H/√3
Using H = D/√3
=> D - 15 = D/3
=> 3D = 45 = D
=> 2D = 45
Distance between Lamp posts = 45 m
Height of Lamp posts = D/√3 = 45/2√3 = 15√3 / 2 m
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