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: Identify similar 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, $\frac{VY}{VW}=\frac{YZ}{WX}$. We know that $VY = 185$ m, $VW=110$ m, and $YZ = 119.5$ m. Let $WX = x$. Then $\frac{185}{110}=\frac{119.5}{x}$.

Step3: Cross - multiply

Cross - multiplying gives us $185x=110\times119.5$.

Step4: Solve for $x$

$x=\frac{110\times119.5}{185}=\frac{13145}{185}\approx71.054$ m. Rounding to the nearest hundredth of a meter, $x\approx71.05$ m.

Answer:

$71.05$ m