A flagpole has a height of 15 yards. It will be supported by three cables, each of which is attached to the flagpole at a point 3 yards below the top of the pole and attached to the ground at a point that is 9 yards from the base of the pole. Find the total number of yards of cable that will be required.
The flagpole will be supported by a total of of cable. (Round to the nearest whole number as needed.)
Answer
Final Answer: The total number of yards of cable that will be required is \(\boxed{45}\).
Step 1 ：Given a flagpole with a height of 15 yards, it will be supported by three cables. Each cable is attached to the flagpole at a point 3 yards below the top of the pole and attached to the ground at a point that is 9 yards from the base of the pole.
Step 2 ：We can use the Pythagorean theorem to calculate the length of each cable. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 3 ：In this case, the length of the flagpole from the ground to the point where the cable is attached (15 - 3 = 12 yards) and the distance from the base of the pole to the point where the cable is attached to the ground (9 yards) form the two sides of the right triangle. The cable forms the hypotenuse.
Step 4 ：Using the Pythagorean theorem, the length of each cable is \(\sqrt{(12^2 + 9^2)}\) yards.
Step 5 ：Since there are three cables, the total length of the cable required is \(3 \times \sqrt{(12^2 + 9^2)}\) yards.
Step 6 ：Final Answer: The total number of yards of cable that will be required is \(\boxed{45}\).
