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GB-37-02-001 · Navigation with Pythagoras

From P, a boat sails 5 km north then 21 km east to Q.

(a) Find the direct distance PQ to 1 decimal place.

(b) Find the bearing of Q from P to the nearest degree. Give a three-figure bearing.

Part (a) Bearings with Pythagoras & SOH CAH TOA Booklet p. 34 & p. 91
Method
1) Use Pythagoras H² = A² + B² for distance PQ
2) Use tan(θ) = Opposite(East) ÷ Adjacent(North) and write bearing as 3 digits from North
Worked Example (GB-37-02-001 · Part (a))
Find the direct distance PQ to 1 decimal place.
1)
52+212\sqrt{5^2+21^2}
2)
21.6 km
Ans = 21.6 km
Part (b) Bearings with Pythagoras & SOH CAH TOA Booklet p. 34 & p. 91
Method
1) Use Pythagoras H² = A² + B² for distance PQ
2) Use tan(θ) = Opposite(East) ÷ Adjacent(North) and write bearing as 3 digits from North
Worked Example (GB-37-02-001 · Part (b))
Find the bearing of Q from P to the nearest degree. Give a three-figure bearing.
1)
tan⁡θ=21/5\tan\theta=21/5
2)
077°
Ans = 077°