Question

Hockey Goals?

Answer 1

Q39: The goalie can stand `13.75` ft from the goal.

Q40: The goalie can stand `19.25` ft from the goal.

Explanation:

It is easy to miss the fact that another distance is given which is not in the diagram.

For Q39, A is a distance of `25`ft from the goal.

The two triangles formed from A and the width of the goalie and from A and the width of the goal are similar triangles.

They both have the common angle at A and a `90°` angle.

Therefore their sides are in the same ratio.

If the distance from A to the goalie is `x`, then we have:

`x/2.7 = 25/6`

`x = (2.7xx25)/6`

`x= 11.25` ft

The distance from the goalie from the goals is :

`25-11.25=13.75`ft

For Q40, the distance of A from the goals is `35`ft.

The calculation is identical:

`x/2.7 = 35/6`

`x = (2.7xx35)/6`

`x =15.75` ft

The goalie must stand `35-15.75 = 19.25`ft

The comparison between the two situations shows that
The further A is from the goals, the further the goalie needs to move out to cover the goal completely.