A ship travels 10 km on a course heading 50º east of north.
How far north, and how far east has the ship travelled at this point?
Answers
Answer:
According to trigonometric identities we know that :
sin theta = ( side opposite to theta ) / ( longest side )
In Δ given :
Side opposite to 40° is y .
Longest side is 10 km .
Hence we can write that :
sin 40 = y / 10
sin 40 = 0.641 [ approx ]
⇒ 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 approximately .
For verification :
x² + y² = 100
⇒ (7.66)² + (6.43)²
⇒ 100.02 approx .
It is not accurate but approximate .
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