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.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )