Question

find the unknown length in the right triangle. image of a right triangle with one leg 15 cm, hypotenuse 18 cm, and the other leg unknown (marked ?). the unknown length is approximately 10 centimeters. (type a whole number or decimal rounded to the nearest thousandth as needed.)

one or more of your responses is incorrect.
at least one of your answers is incorrect. to find the unknown length, use the pythagorean theorem, which states that in any right triangle, (leg)² + (other leg)² = (hypotenuse)². observe the units of the given lengths and select the correct units of the unknown length.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is hypotenuse, \(a\) and \(b\) are legs. Here, hypotenuse \(c = 18\) cm, one leg \(a=15\) cm, unknown leg \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 18\) and \(a = 15\) into formula: \(b=\sqrt{18^{2}-15^{2}}=\sqrt{324 - 225}=\sqrt{99}\).

Step3: Calculate \(\sqrt{99}\)

\(\sqrt{99}\approx9.94987\approx9.950\) (rounded to nearest thousandth) or \(\approx9.95\) (rounded to nearest hundredth) or \(\approx10.0\) (rounded to nearest tenth), but more accurately \(\approx9.95\) or \(\approx9.950\). Wait, wait, no: \(18^2=324\), \(15^2 = 225\), \(324-225 = 99\), \(\sqrt{99}\approx9.94987\), so approximately \(9.95\) (or \(9.950\) if to nearest thousandth). Wait, maybe the initial wrong answer was 10, but correct is around 9.95. Wait, let's recalculate: \(18^2 = 324\), \(15^2=225\), \(324 - 225=99\), \(\sqrt{99}\approx9.94987\), so approximately \(9.95\) (or \(9.950\) when rounded to nearest thousandth).

Answer:

The unknown length is approximately \(\boldsymbol{9.950}\) (or \(\boldsymbol{9.95}\) or \(\boldsymbol{10.0}\) depending on rounding, but more accurately \(\boldsymbol{9.950}\)) centimeters.