Question

to indirectly measure the distance across a lake, isaac makes use of a couple landmarks at points w and x. he measures vy, yw, and yz as marked. find the distance across the lake (wx), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.)

Explanation:

Step1: Prove similarity of triangles

Triangles $\triangle VYZ$ and $\triangle VWX$ are similar because $\angle V$ is common and $\angle VWX=\angle VYZ = 90^{\circ}$.

Step2: Set up proportion

For similar - triangles, the ratios of corresponding sides are equal. So, $\frac{VW}{VY}=\frac{WX}{YZ}$. We know that $VW = 110$ m, $VY=155$ m, and $YZ = 119.75$ m. Substituting these values into the proportion $\frac{110}{155}=\frac{WX}{119.75}$.

Step3: Solve for $WX$

Cross - multiply: $155\times WX=110\times119.75$. Then $WX=\frac{110\times119.75}{155}$.
$110\times119.75 = 13172.5$. And $\frac{13172.5}{155}=85$.

Answer:

$85$ m