Question

an airplane is 1500 ft in the air 2 miles north and 6 miles west of where it took off. 8. a. determine the horizontal distance, h, the plane is from its point of take - off. round to one decimal place. hint: use the pythagorean theorem.

Explanation:

Step1: Apply the Pythagorean Theorem

The Pythagorean Theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\). Here, \(a = 2\) miles and \(b=6\) miles, and \(h\) (the hypotenuse of the right - triangle formed by the north and west distances) is given by \(h^{2}=2^{2}+6^{2}\).

$$h^{2}=4 + 36$$

$$h^{2}=40$$

Step2: Solve for \(h\)

Take the square root of both sides: \(h=\sqrt{40}\).

$$h = 2\sqrt{10}\approx6.3$$

(rounded to one decimal place)

Answer:

\(h\approx6.3\) miles