Question

to indirectly measure the distance across a lake, moussa makes use of a couple landmarks at points d and e. he measures cf, fd, and fg as marked. find the distance across the lake (de), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.)

Explanation:

Step1: Identify similar triangles

Triangles $\triangle CFG$ and $\triangle CDE$ are similar because $\angle CFG=\angle CDE = 90^{\circ}$ and $\angle C$ is common to both triangles.

Step2: Set up proportion

For similar - triangles, the ratios of corresponding sides are equal. That is, $\frac{FG}{DE}=\frac{CF}{CD}$. We know that $FG = 14.2$ m, $CF = 210$ m, and $CD=70$ m.

Step3: Solve for $DE$

From $\frac{FG}{DE}=\frac{CF}{CD}$, we can cross - multiply to get $DE\times CF=FG\times CD$. Then $DE=\frac{FG\times CD}{CF}$.
Substitute the given values: $DE=\frac{14.2\times70}{210}$.
First, calculate $14.2\times70 = 994$. Then $DE=\frac{994}{210}\approx4.73$ m.

Answer:

$4.73$ m