25 points
one particular 13-foot tall cone of dry sand has a base diameter of 38.6 feet. to the nearest tenth of a degree, what is the angle of repose of this type of dry sand?
a different conical pile of the same type of sand as before (which will have the same angle of repose) is 10 feet tall. what is the diameter of the cone’s base?
show your mathematical steps and explain your process in words.

See the attached figure to better understand the problem

we know that

Part A)
in the triangle ABC
C=angle of repose
tan C=AB/BC
AB=13 ft
BC=38.6/2----> BC=19.3 ft

tan C=AB/BC-----> tan C=13/19.3-----> 0.6736
C=arc tan(0.6736)------> C=33.96°-------> C=34°

the answer part A) is
the angle of repose is 34°

Part B)
if
C=34°
AB=10 ft
BC=?
tan C=AB/BC------> BC=AB/tan C-----> BC=10/tan 34-----> BC=14.83 ft

the diameter of the cone base is 2*BC-----> 14.83*2=29.66 ft

the answer Part B) is
the diameter of the cone base is 29.66 ft