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 1 out of 2 hi =

Explanation:

Step1: Identify similar triangles

Triangles $\triangle HJI$ and $\triangle GJK$ are similar because $\angle HJI=\angle GJK = 90^{\circ}$ and $\angle JHI=\angle JGK$ (corresponding - angles, since the lines are parallel in the context of the indirect - measurement setup).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{HI}{GK}=\frac{HJ}{GJ}$. We know that $HJ = 105$ m, $GJ=175$ m, and $GK = 119.6$ m.

Step3: Solve for $HI$

Cross - multiply the proportion: $HI=\frac{HJ\times GK}{GJ}$. Substitute the given values: $HI=\frac{105\times119.6}{175}$.
First, calculate $105\times119.6 = 105\times(120 - 0.4)=105\times120-105\times0.4=12600 - 42 = 12558$.
Then, $HI=\frac{12558}{175}=71.76$ m.

Answer:

$71.76$ m