Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:

Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 13 feet, AC is labeled 15 feet, EC is labeled 10 feet, and ED is labeled 4 feet.
What is the approximate distance, in feet, between the two poles? (5 points)

11.14 feet

16.65 feet

14.35 feet

15.59 feet

1 answer

To find the approximate distance between the two poles, we can use the Pythagorean theorem on the right triangle CED.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In triangle CED, CD is the hypotenuse, with a length of 10 feet, and ED has a length of 4 feet. We can find the length of CD as follows:

CD^2 = EC^2 + ED^2
CD^2 = 10^2 + 4^2
CD^2 = 100 + 16
CD^2 = 116

To find the length of CD, we can take the square root of both sides:

CD = sqrt(116)
CD ≈ 10.77 feet

Now, the distance between the two poles is the sum of AC and CD:

Distance = AC + CD
Distance = 15 + 10.77
Distance ≈ 25.77 feet

Therefore, the approximate distance between the two poles is 25.77 feet. However, none of the given answer choices match this result.

There might have been an error in the given information or in the question. Please check for any mistakes or provide additional information to solve the problem accurately.