Question

to indirectly measure the distance across a lake, fawzia makes use of a couple landmarks at points h and i. she measures gj, jh, and jk as marked. find the distance across the lake (hi), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.) answer attempt 2 out of 2 hi =

Explanation:

Step1: Identify similar triangles

Triangles $\triangle GJH$ and $\triangle GKI$ are similar because $\angle GJH=\angle GKI = 90^{\circ}$ and $\angle JGH=\angle KGI$ (common - angle). By the AA (angle - angle) similarity criterion, the two triangles are similar.

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{JH}{KI}=\frac{GJ}{GK}$. We know $JH = 105$ m, $GJ = 175$ m, and $JK=119.6$ m, then $GK=GJ + JK=175 + 119.6=294.6$ m. Let $KI = x$. The proportion becomes $\frac{105}{x}=\frac{175}{294.6}$.

Step3: Solve the proportion for $x$

Cross - multiply: $175x=105\times294.6$. Then $x=\frac{105\times294.6}{175}$.
$105\times294.6 = 105\times(294 + 0.6)=105\times294+105\times0.6=30870+63 = 30933$.
$x=\frac{30933}{175}=176.76$ m.

Answer:

$176.76$