Question

find m.
write your answer as a whole number or a decimal. do not round.
m = \boxed{} meters

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle MNL\sim\triangle MJK\) (by AA similarity, as \(\angle M\) is common and \(\angle MNL=\angle MJK = 90^{\circ}\)), we can use the proportion \(\frac{NL}{JK}=\frac{MN}{MJ}\).

Step2: Substitute the values

We know that \(NL = 27.3\) m, \(MN=56\) m, and \(MJ=56 + 24=80\) m. Let \(JK = m\). Then the proportion becomes \(\frac{27.3}{m}=\frac{56}{80}\).

Step3: Solve for \(m\)

Cross - multiply: \(56m=27.3\times80\). First, calculate \(27.3\times80 = 2184\). Then \(m=\frac{2184}{56}\).

Step4: Perform the division

\(m = 39\)

Answer:

\(39\)