A rope is used to hold a tree upright. it is attached to the ground at a distance of 95 feet from the tree and forms an angle of 47 degree with the ground. How long is the rope to the nearest foot?
if the rope is length x,
95/x = cos 47°
plug & chug
54
To find the length of the rope, we can use trigonometry. In this case, we have a right triangle formed by the rope, the ground, and the distance from the tree to the rope attachment point on the ground.
Let's call the length of the rope "x". The distance from the tree to the rope attachment point is 95 feet. The angle between the ground and the rope is 47 degrees.
Using the trigonometric function cosine (cos), we can relate the adjacent side (95 feet) and the hypotenuse (the length of the rope):
cos(angle) = adjacent / hypotenuse
cos(47°) = 95 / x
To solve for x, we can rearrange the equation:
x = 95 / cos(47°)
Using a calculator, we can find the value of the cosine of 47 degrees, which is approximately 0.682.
x = 95 / 0.682
Calculating this division, we find that x is approximately 139.24 feet.
Therefore, the length of the rope to the nearest foot is 139 feet.