Question

to indirectly measure the distance across a lake, kayden makes use of a couple landmarks at points p and q. he measures or, rp, and rs as marked. find the distance across the lake (pq), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.) answer attempt 2 out of 2 pq =

Explanation:

Step1: Identify similar triangles

Triangles $\triangle OPR$ and $\triangle OQS$ are similar because $\angle OPR=\angle OQS = 90^{\circ}$ and $\angle O$ is common to both triangles.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, $\frac{PQ}{RS}=\frac{OP}{OR}$. We know that $OP = OR + RP$. Given $RP = 100$ m, $OR=130$ m and $RS = 129.2$ m. First, $OP=130 + 100=230$ m. Then, from $\frac{PQ}{129.2}=\frac{230}{130}$.

Step3: Solve for $PQ$

Cross - multiply to get $130\times PQ=129.2\times230$. Then $PQ=\frac{129.2\times230}{130}$.
$PQ=\frac{29716}{130}\approx228.58$ m.

Answer:

$228.58$ m