A tent pole that is 5 feet tall is secured to the ground with a piece of rope that is 13 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
a) 12 feet
b) 8 feet
c) 25 feet
d) 30 feet
To determine the number of feet from the tent pole to the rope along the ground, we can use the Pythagorean theorem.
The length of the rope is the hypotenuse of a right triangle, with the height of the tent pole being one of the legs.
Using the Pythagorean theorem, we have:
(Length of rope)^2 = (Height of tent pole)^2 + (Distance from tent pole to rope along the ground)^2
Substituting the given values, we have:
13^2 = 5^2 + (Distance from tent pole to rope along the ground)^2
169 = 25 + (Distance from tent pole to rope along the ground)^2
144 = (Distance from tent pole to rope along the ground)^2
Taking the square root of both sides, we get:
Distance from tent pole to rope along the ground = √144
Distance from tent pole to rope along the ground = 12 feet
Therefore, the correct answer is:
a) 12 feet