Answered

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5. Consider the image below of a pasture at McDonald's Farm.
750 ft
45°
Part A: If McDonald wants to fence in the square pasture and barbed-wire
fencing costs $1.15 per foot, then determine the cost to fence in
the pasture.
Part B: If McDonald wants to cover the square pasture in fertilizer, then he
needs to determine the area of the pasture. What is the area of
the pasture to the nearest hundredth?

5 Consider The Image Below Of A Pasture At McDonalds Farm 750 Ft 45 Part A If McDonald Wants To Fence In The Square Pasture And Barbedwire Fencing Costs 115 Per class=

Sagot :

Answer:

Step-by-step explanation:

View image zoedubclub

The area of the square pasture is given by the leg length of the right

triangle which is the same as the side length of the square.

Correct responses:

  • Part A: $2,439.5
  • Part B: 281, 250 ft.²

Method by which the above responses are obtained

Part A

The given triangular side is a right triangle.

Length of the hypotenuse and an acute angle of the right triangle are;

750 ft. and 45°

Therefore;

Leg length of the right triangle = Side length of the square

Leg length of the right triangle = 750 ft. × sin(45°) = 375·√2 ft.

Side length of the square pasture, s = 375·√2 ft.

Perimeter of the fence = 4 × 375·√2 ft. = 1500·√2 ft.

Cost per foot for fencing = $1.15

  • The cost to fence the square pasture = $1.15/ft. × 1,500·√2 ft. ≈ $2,439.5

Part B:

The area, A, of the square pasture is given by A = s²

Which gives;

A = (375·√2)² = 281,250

  • The area of the square pasture is A = 281,250 ft.²

Learn more about trigonometric ratios here:

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