Question

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

Explanation:

Step1: Find \(KN\) using Pythagoras' theorem in \(\triangle KNM\)

In right - triangle \(KNM\), by Pythagoras' theorem \(KN=\sqrt{KM^{2}-NM^{2}}\). Given \(KM = 65\) and \(NM=16\), then \(KN=\sqrt{65^{2}-16^{2}}=\sqrt{(65 + 16)(65 - 16)}=\sqrt{81\times49}=\sqrt{81}\times\sqrt{49}=9\times7 = 63\).

Step2: Find \(LN\) using Pythagoras' theorem in \(\triangle KNL\)

In right - triangle \(KNL\), by Pythagoras' theorem \(LN=\sqrt{KL^{2}-KN^{2}}\). Given \(KL = 105\) and \(KN = 63\), then \(LN=\sqrt{105^{2}-63^{2}}=\sqrt{(105 + 63)(105 - 63)}=\sqrt{168\times42}=\sqrt{42\times4\times42}=42\sqrt{4}=84\).

Answer:

\(84\)