Final answer:
To calculate the length of the steel cable, we use the Pythagorean theorem to find the hypotenuse of the right-angled triangle formed between the pole, the ground, and the cable. Upon calculation, the length of the steel cable is found to be approximately 21.9 feet, closest to 21 feet (Option C).
Step-by-step explanation:
The student is asking for the length of a steel cable that is attached from the top of a telephone pole to the ground, forming a right-angled triangle with the pole and the ground. To find the length of the cable, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, the telephone pole represents one side of the triangle and is 20 feet tall, which we will consider as 'a'. The distance from the pole to where the cable is anchored, which is 9 feet, will be considered as 'b'. The cable itself is the hypotenuse 'c'.
The Pythagorean theorem can be written as:
a2 + b2 = c2
Plugging in our numbers, we get:
202 + 92 = c2
400 + 81 = c2
481 = c2
By taking the square root of both sides, we find that:
c = √481
c ≈ 21.9 feet
Therefore, the closest answer to the length of the steel cable is 21 feet (Option C).