Question

A youth group is setting up camp. Rain is predicted, so the campers decided to build a fly, or rain cover, over their tent. The fly will be 12 feet high and 16 feet wide. The scouts are building the frame for the fly with two poles slanted and joined together at the top of the tent

The minimum length of the slanted piles needed to support the fly is____ feet.

Answer 1

14.42  i think is the correct answer

Answer 2

14.422 feet

Explanation:

The campers decided to build a fly, or rain cover, over their tent.

The fly will be 12 feet high and 16 feet wide.

Refer the attached figure

AD =12 feet

BC = 16 feet

The fly is in the shape of cone we take cut section of it in the form of triangle.

So, the triangle is isosceles triangle .

Since AD is the perpendicular bisector of the isosceles triangle .So, BD = DC

So, D is the midpoint of BC

So, BD= DC=
`(BC)/(2)`

BD= DC=
`(16)/(2)`

BD= DC= 8

So, we will use Pythagoras theorem in ΔADC

`Hypotenuse^2=Perpendicular^2+Base^2`

`AC^2=AD^2+DC^2`

`AC^2=12^2+8^2`

`AC^2=144+64`

`AC^2=208`

`AC=√(208)`

`AC=14.422`

The minimum length of the slanted piles needed to support the fly is 14.422 feet.