Question

an airpl takes off, levels off, and lands according to the diagram shown below. you might need: calculator all me ments listed are in kilometers. what is the horizontal distance from the planes starting position to its finishing position? round your answer to the nearest tenth of a kilometer. kilometers show calculator

Explanation:

Step1: Find the value of \(x\) using the Pythagorean theorem

For the right - triangle with hypotenuse \(5\) and height \(3\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 5\), \(b = 3\), and \(a=x\). So \(x=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\).

Step2: Find the value of \(y\) using the Pythagorean theorem

For the right - triangle with hypotenuse \(7\) and height \(3\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 7\), \(b = 3\), and \(a = y\). So \(y=\sqrt{7^{2}-3^{2}}=\sqrt{49 - 9}=\sqrt{40}\approx6.3\).

Step3: Calculate the total horizontal distance

The total horizontal distance \(D=x + 3+3+y\). Substitute \(x = 4\) and \(y\approx6.3\) into the formula. \(D=4+3 + 3+6.3=16.3\).

Answer:

\(16.3\) kilometers