Question

question to indirectly measure the distance across a lake, rashad makes use of a couple landmarks at points l and m. he measures kn, nl, and no as marked. find the distance across the lake (lm), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.)

Explanation:

Step1: Identify similar triangles

$\triangle KNO \sim \triangle KLM$ (right triangles, shared $\angle K$)

Step2: Set up proportion

$\frac{LM}{NO} = \frac{KL}{KN}$
Substitute values: $\frac{LM}{111.15} = \frac{100+185}{185}$

Step3: Simplify denominator

$100+185=285$, so $\frac{LM}{111.15} = \frac{285}{185}$

Step4: Solve for $LM$

$LM = 111.15 \times \frac{285}{185}$
Calculate $\frac{285}{185} \approx 1.5405$
$LM \approx 111.15 \times 1.5405$

Step5: Compute final value

$LM \approx 171.23$

Answer:

171.23 meters