Question

One particular 33 feet tall cone dry sand has a base diameter of 97.8 feet. To the nearest tenth of a degree, what is the angle of repose of this type of dry sand?

Answer 1

This forms a right triangle with height = 33 and side = 48.9

arc tan (angle) = 33/48.9

arc tan (angle) = 0.6748466258

angle = 34.0 Degrees

Explanation:

Answer 2

Angle of repose of the cone of dry stand is 34.0°

Explanation:

Angle of repose of a cone shaped mountain is the angle between base of the mountain and height as shown in the figure attached.

From the triangle ABC,

tanB =
`(AD)/(BD)`

=
`(AD)/((BC)/(2))`

=
`(33)/((97.8)/(2) )`

=
`(66)/(97.8)`

tanB = 0.6748

B =
`tan^(-1)(0.6748)`

= 34.01°≈ 34.0°

Therefore, angle of repose of the cone of dry stand is 34.0°