Question

a tent maker wishes to support a 13-ft tent wall by attaching cable to the top of it, and then anchoring the cable 7 feet from the base of the tent. how long of a cable is needed? round your answer to the nearest tenth of a foot, but do not include \ft\ with your response. answer

Explanation:

Step1: Identify the right triangle

The tent wall, the ground from the base to the anchor, and the cable form a right triangle. The tent wall (13 ft) and the ground segment (7 ft) are the legs, and the cable is the hypotenuse. We use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 13 \), \( b = 7 \).

Step2: Calculate \( a^2 + b^2 \)

\( a^2 = 13^2 = 169 \), \( b^2 = 7^2 = 49 \). Then \( a^2 + b^2 = 169 + 49 = 218 \).

Step3: Find the square root

\( c = \sqrt{218} \approx 14.8 \) (rounded to the nearest tenth).

Answer:

14.8