Finding the radius based on height of my building and max angle of repose? height: 20 feet length: 200 feet width: 120 feet material: sand, bank damp ( angle of repose is 45 degrees) sand, bank dry ( angle of repose is 35 degrees) sand, core ( angle of repose 41 degrees) sand, foundry prepared ( 30 - 44 degrees) sand, foundry shakeout (39 degrees)

The maximum angle of repose is the maximum angle at which a material can be piled without slumping. The material piled up will form a cone.

If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).

Recalling trigonometry formulae:
tanα = O / A

Solving for A:
A = O / tanα

We can now substitute our data (O = 20):
1) Sand, Bank Damp 
α = 45° 
A = 20 / tan(45)
   = 20
The radius is 20 feet.

2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
   = 28.5629
The radius is 28.6 feet.

3) Sand, core 
α = 41°
A = 20 / tan(41)
   = 23.0074
The radius is 23 feet.

4) Sand, foundry prepared 
α₁ = 30°
A₁ = 20 / tan(30)
   = 34.6410

α₂ = 44°
A₂ = 20 / tan(44)
   = 20.7106

The radius is between 20.7 and 34.6 feet.

5) Sand, Foundry shakeout 
α = 39°
A = 20 / tan(39)
   = 24.6979

The radius is 24.7 feet.

He estimated that he had about $9 worth of groceries

Step-by-step explanation:

Given that

Gallon of milk =  $3.49

Three pounds of  oranges = $1.14(3) = $3.42

Box of cereal =  $3.46

Here the front end estimation should be applied that means only considered the number that shows in the front side and the remaining numbers should be zeros

Now applying the front end estimation, It shows like this

$3.49 => $3.00

$3.42 => $3.00

$3.46 => $3.00

Now sum of all 3 that comes 9

Therefore the second option is correct