John walked 11m to the north, then he turns north-east and walks 21√2m,next he moves 135° clockwise and moves 27m.finally he turns right and moves 16m.how far is he from his starting point?
A) 5√2m
B) 6√2m
C) 7√2m
D) 8√2m
Answers
Given : John walked 11m to the north, then he turns north-east and walks 21√2m, next he moves 135° clockwise and moves 27m.finally he turns right and moves 16m.
To Find : how far is he from his starting point
A) 5√2m
B) 6√2m
C) 7√2m
D) 8√2m
Solution:
NORTH
WEST EAST
SOUTH
John walked 11 m to the north
NORTH = 11 km
he turns north-east and walks 21√2m,
=> 45° anticlockwise
EAST = 21√2Cos45° = 21 m
NORTH = 21√2Sin45° = 21 m
he moves 135° clockwise Hence
45° - 135° = -90° ( means South Direction )
EAST = 27 Cos(-90) = 0
NORTH = 27 Sin(-90) = - 27
turns right means WEST
WEST = 16 m = EAST - 16 m
NORTH = 11 + 21 - 27 = 5
EAST = 21 + 0 -16 = 5
North = 5 m
East = 5 m
Distance from starting point = √5² + 5²
= 5√2
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