A man walks 1km due east and then 1km due north. His displacement is

Jamb 1978

A man walks 1km due east and then 1km due north. His displacement is 

A. 1km N15°E

B. 1km N30°E

C. √2km N45°E

D. √2km N60°E

E. 2km N75°E

ANSWER: Option C

EXPLANATION: His displacement is the shortest distance from his starting point, so, the hypotenuse represent his displacement. Using the four cardinal point diagram, mark 1km due east on the diagram and the from that point, 1km due North, and then join the start and the end point together to form a right-angled triangle! Then solve using Pythagoras theorem or triangle method to find your displacement and using SOHCAHTOA, you can find the angle of displacement or the direction.

Pythagoras theorem

Hyp² = opp² + adj²

SOHCAHTOA means 

Sin ∅ = Opp/hyp

Cos ∅ = adj/hyp

Tan ∅ = opp/adj

Using any of those, you will have the same answer for your direction.

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