Question

if ( jk = 23 ), ( ki = 15 ), and ( nl = 22 ), find the length of ( overline{mn} ). round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
answer attempt 1 out of 2
( mn=)

Explanation:

Step1: Determine similarity of triangles

Since the angles of triangle \(JKI\) (\(58^{\circ},81^{\circ},41^{\circ}\)) and triangle \(MNL\) (\(58^{\circ},81^{\circ},41^{\circ}\)) are equal, \(\triangle JKI\sim\triangle MNL\) (by AA - Angle - Angle similarity criterion).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. \(\frac{JK}{MN}=\frac{KI}{NL}\).
Given \(JK = 23\), \(KI = 15\), and \(NL = 22\). Substitute the values into the proportion: \(\frac{23}{MN}=\frac{15}{22}\).

Step3: Solve for \(MN\)

Cross - multiply: \(15\times MN=23\times22\). Then \(MN=\frac{23\times22}{15}\).
Calculate \(23\times22 = 506\). So \(MN=\frac{506}{15}\approx33.7\).

Answer:

\(33.7\)