Question

Farming. An auger used to deliver grain to a storage bin can be raised and lowered, thus allowing for different size bins. Let a be the

angle formed by the auger and the ground for bin A such that tana =
35
12
half of a. If the height h, in feet, of a bin can be found using the formula h
auger, find the height of bin B.
The angle formed by the auger and the ground for bin Bis
= 65 sin0, where is the angle formed by the ground and the
Round your answer to the nearest integer.
h =
ft

Answer 1

The height of the bin B is 38 feet.

How the height of the bin B is calculated.

Given that

tan α = 35/12

height of bin B = 65 sin θ

θ = α/2 (angle formed by the auger and the ground for bin B).

Let's calculate

tanα = 35/12

α = tan⁻¹(35/12)

α = 71.08⁰

But

θ = α/2

θ = 71.08/2

= 35.54⁰

Calculate the height of bin B using the formula:

h = 65 * sin(θ)

Substituting the value of θ, we get:

h = 65 * sin(α/2)

h = 65sin(θ)

h ≈ 65 *sin(35.54)

= 65 *0.5812

= 37.78 feet

≈ 38 feet

The height of the bin B is 38 feet.