Steve and Peggy want to rent a 40 ft x 20 ft tent for their backyard to host a barbecue. The base of the tent is supported 7 ft above the ground by poles and the roped stakes are used for support. The ropes make a 60 degree angle with the ground. What are the dimensions of the rectangle formed by the stakes on the ground?
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a tree needs to be staked down before a storm. if the ropes can be tied on the tree trunk 17 feet above the ground and the staked rope should make a 60 degree angle with the ground, how far from the base of the tree should each rope be staked
Since the ropes make an angle of 60°, they extend x feet past the tent poles,
7/x = tan 60° = √3
x = 7/√3 = 4
Assuming that there are two stakes at each corner, extending both the length and the width by 4 feet, our stake rectangle has dimensions
40+8 by 20+8 = 48x28 ft
To find the dimensions of the rectangle formed by the stakes on the ground, we can start by finding the length of each side.
Given that the base of the tent is supported 7 ft above the ground by poles, we can use this information to find the length of the sides.
We know that the angle formed by the ropes with the ground is 60 degrees. Since we have a right-angled triangle formed by the ground, one of the ropes, and the pole, we can use trigonometry to find the length of the sides.
Let's denote the length of one side of the rectangle as x.
Using trigonometry, we can write:
cos(60) = adjacent/hypotenuse
cos(60) = x/7
Simplifying the equation:
0.5 = x/7
Multiplying both sides by 7:
7 * 0.5 = x
3.5 = x
So, the length of one side of the rectangle formed by the stakes is 3.5 ft.
Since the tent is a 40 ft x 20 ft rectangle, the dimensions of the rectangle formed by the stakes on the ground are 3.5 ft x 3.5 ft.
To find the dimensions of the rectangle formed by the stakes on the ground, we can use trigonometry.
Let's call the length of the rectangle "x" and the width of the rectangle "y".
From the given information, we know that the base of the tent is 7 ft above the ground, and the ropes make a 60-degree angle with the ground.
Using trigonometry, we can find:
y = 7 ft * tan(60 degrees)
y = 7 ft * √3
Next, we can find the value of "x" using trigonometry as well. Since the base of the tent is 40 ft, and the angle formed by the tent poles and the ropes is 90 degrees (right angle), we have a right triangle. The base (40 ft) is the adjacent side, and the height (7 ft) is the opposite side.
Using the Pythagorean theorem:
x^2 = (40 ft)^2 - (7 ft)^2
x^2 = 1600 ft^2 - 49 ft^2
x^2 = 1551 ft^2
x = √1551 ft
Therefore, the dimensions of the rectangle formed by the stakes on the ground are approximately:
Length (x) = √1551 ft
Width (y) = 7 ft * √3
Please note that these are approximate values, and you can round them according to your desired precision.