The ship travels 6.43 km towards north and 7.66 km towards the east from the point where the ship was headed. This can be verified from the Pythagoras theorem.
What is displacement?
Displacement is the change in the position of the ship in water. This can be calculated through trigonometric identities.
According to trigonometric identities we know that:
sinФ = ( side opposite to Ф ) / ( longest side )
Side opposite to 40° is y
Longest side is 10 km
Hence we can write that:
sin 40 = y / 10
sin 40 = 0.641
0.643 = y/10
y = 0.643 × 10
y ≈ 6.43 km
The value of y is approximately 6.43 km
Now we know that by Pythagoras theorem:
x² + y² = 10²
x² + ( 6.43 )² = 100
x² = 100 - 41.345
x² = 58.655
x ≈ 7.66 km
The value of x is approximately 7.66 km
The Pythagoras theorem states:
( longest side )² = ( base )² + ( height )²
The theorem is applied in right angles
sin 40 is 0.641
For verification:
x² + y² = 100
(7.66)² + (6.43)²
100
Learn more about Pythagoras theorem here:
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