Question

use the information given in the figure to find the length kn.
if applicable, round your answer to the nearest whole number.
the lengths on the figure are not drawn accurately.

Explanation:

Step1: Find the length of \(LN\)

In right - triangle \(LMN\), using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = LM = 25\) and \(b=MN = 20\). Let \(a = LN\).

$$LN=\sqrt{LM^{2}-MN^{2}}=\sqrt{25^{2}-20^{2}}=\sqrt{(25 + 20)(25 - 20)}=\sqrt{45\times5}=\sqrt{225}=15$$

Step2: Find the length of \(KN\)

In right - triangle \(KLN\), using the Pythagorean theorem \(KN=\sqrt{KL^{2}-LN^{2}}\), where \(KL = 17\) and \(LN = 15\)

$$KN=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}=\sqrt{32\times2}=\sqrt{64}=8$$

Answer:

\(8\)