Question

From his house, Manuel could drive due north to get to his parents' house or he could drive due east to get to his grandparents' house. It is 6 miles from Manuel's house to his parents' house and a straight-line distance of 10 miles from his parents' house to his grandparents' house. How far is Manuel from his grandparents' house?

Answer 1

The distance is 8 miles.

Explanation:

Manuel's house, his parents house, and grandparents house can be expressed as the three vertices of a right angled triangle. Thus, Pythagoras theorem can be applied to determine the distance from Manual's house to that of his grandparents.

Let the distance from Manuel's house to that of his grandparents be represented by x, so that;

`/Hyp/^(2)` =
`/Adj 1/^(2)` +
`/Adj 2/^(2)`

`/10/^(2)` =
`/x/^(2)` +
`/6/^(2)`

100 =
`x^(2)` + 36

`x^(2)` = 100 - 36

= 64

⇒ x =
`√(64)`

= 8

x = 8 miles

Thus, Manuel's house is 8 miles from his grandparents house.