Question

a kite flying in the air has a 12 - ft line attached to it. its line is pulled taut and casts an 11 - ft shadow. find the height of the kite. if necessary, round your answer to the nearest tenth. 12 11

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the kite be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 12\) (the length of the line, hypotenuse) and \(a=11\) (the shadow length, one - leg). We need to find \(b = h\). So, \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 12\) and \(a = 11\) into the formula: \(h=\sqrt{12^{2}-11^{2}}=\sqrt{144 - 121}=\sqrt{23}\).

Step3: Calculate the value

\(\sqrt{23}\approx4.8\) (rounded to the nearest tenth).

Answer:

\(4.8\)