Question

1. to determine the distance ab across a pond, surveyors measured the distances shown in the diagram. given that ab || df, determine the distance ab across the pond, to 1 decimal place.4

Explanation:

Step1: Identify similar triangles

Since $AB\parallel DF$, $\triangle CAB\sim\triangle CDF$.

Step2: Set up proportion

The ratio of corresponding sides of similar triangles is equal. So $\frac{AB}{DF}=\frac{CA}{CD}$. We know $CA = 22.5$ m, $CD=22.5 + 63.0=85.5$ m and $DF = 25.7$ m. Substituting these values into the proportion gives $\frac{AB}{25.7}=\frac{22.5}{85.5}$.

Step3: Solve for $AB$

Cross - multiply: $AB\times85.5=25.7\times22.5$. Then $AB=\frac{25.7\times22.5}{85.5}$.
$AB=\frac{578.25}{85.5}\approx6.8$ m.

Answer:

$6.8$ m