Question

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

Explanation:

Step1: Use the similarity of triangles

Since \(\angle P=\angle L = 90^{\circ}\) and \(\angle M\) is common, \(\triangle MLO\sim\triangle MPO\).
For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{ML}{MP}=\frac{s}{OP}\).
Here, \(ML = 30\), \(MP=30 + 15=45\), \(OP = 24\).

Step2: Substitute values into the proportion

Substitute the values into \(\frac{ML}{MP}=\frac{s}{OP}\), we get \(\frac{30}{45}=\frac{s}{24}\).
Cross - multiply: \(45s=30\times24\).
Then \(s=\frac{30\times24}{45}\).
Calculate \(30\times24 = 720\), so \(s=\frac{720}{45}\).
Simplify \(\frac{720}{45}=16\).

Answer:

\(16\)