At 5 p.m. on a sunny day, Sameer starts walking from a park gate with his shadow falling exactly behind him. After 20 m, he turns left and walks 15 m, and then turns left again and walks 28 m. How far and in which direction is he from the park gate? (The Sun sets in the West.)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 17 m South-East
In the evening the Sun is in the West, so shadows fall towards the East. A shadow exactly behind him means his back is to the East. A left turn moves the facing direction one step anticlockwise (West → South → East).
Shadow behind him points East, so he starts walking West
Facing West, 20 m: 20 m west of the gate
Turns left, now facing South, 15 m: 20 m west, 15 m south
Turns left, now facing East, 28 m: \(28-20=8\) m east, 15 m south
Distance \(=\sqrt{8^{2}+15^{2}}=\sqrt{64+225}=\sqrt{289}=17\) m
He is south and east of the gate, so the direction is South-East
Sameer is 17 m South-East of the park gate.
