Question

From her house, Meg must drive 8 miles due north to visit her aunt. From her house, she must drive 15 miles due east to visit her grandmother. Which is the straight-line distance from Meg's aunt's house to her grandmother's house?

Answer 1

The straight line distance is 17 miles from Meg's aunt's house to her grandmother's house.

Explanation:

We have drawn the diagram for your reference.

Given:

Meg have to drive 8 miles due north to visit her aunt.

From diagram we can say;

BA = 8 miles

Also she has to drive 15 miles due east to visit her grandmother.

From diagram we can say;

BC = 15 miles

We need to find the straight-line distance from Meg's aunt's house to her grandmother's house i.e we need to find AC from diagram.

Now We can Assume it as a right angled triangle.

So Pythagoras theorem we can say that;

`AC^2= AB^2+BC^2\\\\AC^2 =8^2+15^2= 64+225 =289`

Now taking Square root on both side we get;

`√(AC^2)= √(289) \\ \\AC =17 \ miles`

Hence The straight line distance is 17 miles from Meg's aunt's house to her grandmother's house.