Final answer:
To find the area that the horse can graze, we need to calculate the area of the sector formed by the length of the rope. Using trigonometry, we can find the angle between the rope and one side of the rectangle, and then substitute it into the formula for the area of a sector.
Step-by-step explanation:
To calculate the area that the horse can graze, we need to find the area of the sector formed by the length of the rope. The formula to find the area of a sector is given by A = (θ/360) * π * r^2, where θ is the angle in degrees and r is the length of the radius. In this case, the radius is the length of the rope, which is 21 m.
To find the angle θ, we can use the property that the angle between the rope and one side of the rectangle is equal to the angle between the rope and the adjacent side of the rectangle.
Using trigonometry, we can calculate the angle θ as θ = sin^(-1)(d/r), where d is the length of one side of the rectangle and r is the length of the rope. Once we have the angle θ, we can substitute it into the formula for the area of the sector to calculate the area that the horse can graze.
In this case, the length of one side of the rectangle is 70 m and the length of the rope is 21 m. So, the angle θ can be calculated as θ = sin^(-1)(70/21) = sin^(-1)(10/3) = 67.38 degrees.
Finally, substituting the values into the formula for the area of the sector, we find that the horse can graze an area of approximately 311.84 square meters.