13. A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, how far away is where it is tied to from the base of the flag pole? Round your answer to the nearest hundredth.
which answer is it of the following:
28.98 ft
108.18 ft
7.25 ft
27.05 ft
To calculate the distance away from the base of the flagpole where the rope is tied, we can use trigonometry. We can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse.
In this case, the opposite side is the distance away from the base of the flagpole where the rope is tied, and the hypotenuse is the length of the rope.
Using the sine function:
sin(15 degrees) = opposite / hypotenuse
sin(15 degrees) = x / 28 ft
Rearranging the equation to solve for x:
x = sin(15 degrees) * 28 ft
Calculating this using a calculator, we find:
x ≈ 7.25 ft
Therefore, the distance away from the base of the flagpole where the rope is tied is approximately 7.25 ft. The correct answer choice is 7.25 ft.