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.
(1 point)
Responses
27.05 ft
27.05 ft
108.18 ft
108.18 ft
7.25 ft
7.25 ft
28.98 ft
To solve this problem, we can use trigonometry. The distance from where the rope is tied to the base of the flag pole can be represented by the adjacent side of a right triangle, where the hypotenuse is the length of the rope (28 ft) and the angle between the rope and the ground is 15 degrees.
Using the cosine function:
cos(15 degrees) = adjacent/hypotenuse
adjacent = cos(15 degrees) * hypotenuse
adjacent = cos(15 degrees) * 28 ft
Using a calculator, we find that cos(15 degrees) is approximately 0.9659.
adjacent = 0.9659 * 28 ft
adjacent ≈ 27.05 ft
Therefore, the distance from where the rope is tied to the base of the flag pole is approximately 27.05 ft.