Question

41 one end of a cable is attached to the top of a flagpole and the other end is attached 6 feet away from the base of the pole. if the height of the flagpole is 12 feet, find the length of the cable. image of a right triangle with vertical side labeled flagpole 12 ft, horizontal side 6 ft, and hypotenuse labeled cable round your answer to the nearest tenth. a 13.4 feet b 13.1 feet c 18 feet d 10.4 feet

Explanation:

Step1: Identify the triangle type

The flagpole, the ground, and the cable form a right triangle. The flagpole height (12 ft) and the ground distance (6 ft) are the legs, and the cable is the hypotenuse. We use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 12 \), \( b = 6 \), and \( c \) is the cable length.

Step2: Apply the Pythagorean theorem

Substitute \( a = 12 \) and \( b = 6 \) into the formula:
\( c = \sqrt{12^2 + 6^2} = \sqrt{144 + 36} = \sqrt{180} \)

Step3: Simplify and round

Calculate \( \sqrt{180} \approx 13.416 \), then round to the nearest tenth: \( 13.4 \)

Answer:

A. 13.4 feet