Question

use the pythagorean theorem. professor ortiz leaves campus on her bike, heading west at 12 ft/sec. professor wilson leaves campus at the same time and walks south at 9 ft/sec. how far apart are they after 10 sec? the professors are □ ft apart after 10 sec.

Explanation:

Step1: Calculate the distance each professor travels

Professor Ortiz travels west at a speed of \(12\) ft/sec for \(10\) sec. Using the formula \(d = vt\) (distance = velocity×time), her distance \(x=12\times10 = 120\) ft.
Professor Wilson travels south at a speed of \(9\) ft/sec for \(10\) sec. Using the formula \(d = vt\), his distance \(y = 9\times10=90\) ft.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(a\) and \(b\) are the legs of a right - triangle and \(c\) is the hypotenuse. Here, \(a = 120\) and \(b = 90\).

$$c=\sqrt{120^{2}+90^{2}}=\sqrt{(120\times120)+(90\times90)}=\sqrt{14400 + 8100}=\sqrt{22500}$$

$$c = 150$$

Answer:

\(150\)