Starting from a bus depot, a van travels 4 km west, turns left and travels 7 km, turns left and travels 12 km, then turns right and travels 8 km. What is the straight-line distance between the van and the depot?

15 kmCorrect answerYour answer17 kmCorrect answerYour answer23 kmCorrect answerYour answer31 kmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Left from west is south; left from south is east; right from east is south.
East–west: 4 km west, then 12 km east, leaving 8 km east.
North–south: $7 + 8 = 15$ km south.
Distance $= \sqrt{8^2 + 15^2} = \sqrt{289} = 17$ km (the 8-15-17 triple).

Worth noting

31 km is the distance driven, and 23 km adds 8 and 15. The common slip is treating the last right turn (from east) as a turn to north; facing east, your right hand points south.

Concept: Four legs, the 8-15-17 triple
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsDistance and final position

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Ten questions from Direction Sense, at your own pace.

Starting from a bus depot, a van travels 4 km west, turns left and travels 7 km, turns left and travels 12 km, then turns right and travels 8 km. What is the straight-line distance between the van and the depot?

Explanation