Question

a kite flying in the air has an 11 - ft line attached to it. its line is pulled taut and casts a 9 - ft shadow. find the height of the kite. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the length of the kite line (11 ft) is the hypotenuse (\(c\)), the length of the shadow (9 ft) is one leg (\(a\)), and the height of the kite (\(b\)) is the other leg. We can use the Pythagorean theorem, which states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), and we want to solve for \(b\). So we can re - arrange the formula to \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

We know that \(c = 11\) and \(a=9\). Substitute these values into the formula: \(b=\sqrt{11^{2}-9^{2}}\). First, calculate \(11^{2}=121\) and \(9^{2} = 81\). Then, \(11^{2}-9^{2}=121 - 81=40\). So \(b=\sqrt{40}\).

Step3: Calculate the square root

\(\sqrt{40}\approx6.3\) (rounded to the nearest tenth).

Answer:

\(6.3\)