Question

a kite is flying 12 ft off the ground. its line is pulled taut and casts a 7-ft shadow. find the length of the line. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

The problem forms a right triangle, where the height (12 ft) and the base (7 ft) are the legs, and the kite line is the hypotenuse. We use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 12\), \(b = 7\), and \(c\) is the hypotenuse (kite line length).

Step2: Apply the Pythagorean theorem

Substitute the values into the formula: \(c = \sqrt{12^2 + 7^2}\). Calculate \(12^2 = 144\) and \(7^2 = 49\). Then, \(144 + 49 = 193\). So, \(c = \sqrt{193}\).

Step3: Calculate the square root

\(\sqrt{193} \approx 13.9\) (rounded to the nearest tenth).

Answer:

13.9