two lamp post are of equal height a boy measure the angle of elevation of the top of East lamppost from the midpoint of the line joining the feel of the lamp post are 30° after walking 15 M towards one of them we measure the angle of elevation of its top at the point where we stand at 60 degree find the height of each lamppost and the distance between them
Answers
Answer:
the distance between lamppost = 45 m
the height of each lamppost = 13 m
Step-by-step explanation:
Let say Height of Lamp Post = H m
Distance between Post = 2D m
=> Distance of mid point from Post = D m
Tan30 = H/D
=> 1/√3 = H/D
=> D = H√3
Tan 60 = H/(D - 15)
=> √3 = H/(D - 15)
=> D√3 - 15√3 = H
=> H√3√3 - 15√3 = H
=> 3H - 15√3 = H
=> 2H = 15√3
H = 15√3/2
the height of each lamppost = 15√3/2 m = 13 m
D = H√3 = 45/2
2D = 45
the distance between lamppost = 45 m
Answer:
the distance between lamppost = 45 m
the height of each lamppost = 13 m
Step-by-step explanation:
Let say Height of Lamp Post = H m
Distance between Post = 2D m
=> Distance of mid point from Post = D m
Tan30 = H/D
=> 1/√3 = H/D
=> D = H√3
Tan 60 = H/(D - 15)
=> √3 = H/(D - 15)
=> D√3 - 15√3 = H
=> H√3√3 - 15√3 = H
=> 3H - 15√3 = H
=> 2H = 15√3
H = 15√3/2
the height of each lamppost = 15√3/2 m = 13 m
D = H√3 = 45/2
2D = 45
the distance between lamppost = 45 m