Question

A hiker leaves camp and using a compass walks 3 km west then 4 km north. How far is the hiker from camp at this point and which direction should be taken to get back to camp?

Answer 1

hi

he is 1km far from the camp

he will walks west 1km to reach

the

camp

Answer 2

Because the hiker walked directly west and then directly north the two legs of the hike forms a right triangle. Therefore we can use the Pythagorean Theorem to solve this problem.

The Pythagorean Theorem states:

c

2

=

a

2

+

b

2

Where:

a

and

b

are legs of the triangle. In this case 3 km and 4 km.

c

is the hypotenuse of the triangle which is what we are trying to solve for in this problem.

Substituting the values from the problem gives:

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

2

=

9

+

16

c

2

=

25

√

c

2

=

√

25

c

=

5

The hiker is 5km from camp and should head in a generally south-east direction