A rope is tied from the top of a flag pulled to the ground. If the rope is 28 feet long and makes a 15° angle with the ground. How far away is it where it is tied to from the base of the flagpole
To solve this problem, we can use trigonometry, specifically the sine function.
The opposite side to the angle of 15° is the height of the flagpole, and the hypotenuse is the length of the rope. We want to find the adjacent side, which is the distance from the base of the flagpole to where the rope is tied.
Using the sine function:
sin(15°) = opposite/hypotenuse
Rearranging the formula to solve for the adjacent side:
adjacent = hypotenuse * sin(15°)
Plugging in the values:
adjacent = 28 feet * sin(15°)
Calculating sine of 15°:
adjacent = 28 feet * 0.2588
Calculating the product:
adjacent ≈ 7.26 feet
Therefore, the rope is tied approximately 7.26 feet away from the base of the flagpole.