Question

A man faces south and walks 10km, turns west and covers 4km, then turns north and covers 7km. He is at a distance of ______ from the starting point.​

Answer 1

Answer:

I think 5 is the answer. Hope I am correct.

Answer 2

Recall the formula of Pythagoras theorem use in Trigonometry:

$a^2 + b^2 = c^2$

See attached for the visual interpretation of the question.

Given:

⇒ First, he went southwards for 10 km

⇒ Then, he went westwards for 4 km

⇒ Finally, he went northwards for 7 km

From the attached diagram, we can see that he started from point A and ended at point E.

⇒ △ABE is a right angle triangle.

Find length of AB:

$\text{AB} = 10 - 7$

$\text{AB} = 3 \text {km}$

Find the length BE:

$\text{BE} = \text{CD}$

$\text{BE} = 4 \text{ km}$

Find the length AE:

$a^2 + b^2 = c^2$

$c^2 = 3^2 + 4^2$

$c^2 = 9 + 16$

$c^2 = 25$

$c = 5$

Find the distance from the end point to the starting point:

$\text {Distance} = \text {AE}$

$\text {Distance} = 5 \text{ km}$

Answer:  He is at a distance of  5km  from the starting point.​