Question

Tim went 8 miles east and 15 miles north. Jan went 5 miles west and 12 miles north. How far apart are they?

Answer 1

30miles

Explanation:

As you can see in the graph, the distance between tim and jan is creating 2 right triangles

You can solve this using pythagoras theorem,

Triangle (1) :

`x^(2) = {5}^(2) + {12}^(2) \\ {x} = \sqrt{{5}^(2) + {12}^(2) } \\ = √(169 ) \\ = 13`

X (1) = 13 miles

Triangle (2):

`{x}^(2) = {15}^(2) + {8}^(2) \\ x = \sqrt{ {8}^(2) + {15}^(2) } \\ = √(289) \\ = 17`

X(2) = 17 miles

Now, the distance = x(1) + x(2)

= 13 + 17

=30 miles

Therefore, Tim and Jan are 30 miles apart