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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
12
half of a. If the height h, in feet, of a bin can be found using the formula h = 75 sine, where is the angle formed by the ground and the
auger, find the height of bin B.

Farming. An auger used to deliver grain to a storage bin can be raised and lowered-example-1

1 Answer

3 votes

The exact value of Cos(x/2) is -√(6-√31)/6.

The height of the bin B is 43.60 ft

How to determine half angle using half angle identity.

Given that sinx = √5/6 and π < x < 3π/2

cosx = +-√(1 - sin²x)

= +-√(1 - (√5/6)²)

= +-√{1 -5/36)

= +-√(31/36)

= +-√31/6

Cosx is negative in the third quadrant

cosx = -√31/6

Cos(x/2) = +-√(1 + cosx/2)

= +-√1 + (-√31/6)/2

= +-√(1 - √31/6)/2

= +-√(6 -√31/6)/2

= +-√(6 - √31)/3

Cos(x/2) = -√(6-√31)/6

2) tanα = 35/12

α = tan⁻¹(35/12)

= 71.06⁰

The angle formed by the auger and the ground for bin B

θ = α/2( it is half α)

The height of bin B using the formula:

h = 75 * sin(θ)

h = 75 * sin(α/2)

θ = α/2 ≈ 71.06/2 ≈ 35.54 degrees

Calculate h:

h = 75 * sin(θ)

h = 75 * sin(35.54)

= 75 * 0.5813

= 43.60 ft

Therefore, the height of the bin B is 43.60 ft.

complete question

Farming. An auger used to deliver grain to a storage bin can be raised and lowered, thus allowing for different size bins. Let α be the angle formed by the auger and the ground for bin A such that tanα = 35/12. The angle formed by the auger and the ground for bin B is

half of α. If the height h, in feet, of a bin can be found using the formula h = 75 sinθ, where θ is the angle formed by the ground and the

auger, find the height of bin B.

User Daniel Placek
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