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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

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

Farming. An auger used to deliver grain to a storage bin can be raised and lowered-example-1
User Avi Avidan
by
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1 Answer

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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 = 65 * sin(θ)

h ≈ 65 * sin(35.54)

= 65 * 0.5812

= 37.78 feet

≈ 38 feet

The height of the bin B is 38 feet.

User Matt Wrock
by
8.0k points