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.)
answer attempt 1 out of 2
wx = in

Explanation:

Step1: Identify similar triangles

Triangles $\triangle VWX$ and $\triangle VYZ$ are similar (both have right angles, share $\angle V$, so AA similarity).

Step2: Set up proportion

Corresponding sides are proportional:
$\frac{WX}{YZ} = \frac{VW}{VY}$
First calculate $VW = VY + YW = 155 + 110 = 265$ m

Step3: Solve for $WX$

Rearrange proportion to isolate $WX$:
$WX = YZ \times \frac{VW}{VY}$
Substitute values: $WX = 113.75 \times \frac{265}{155}$

Step4: Compute the value

Calculate $\frac{265}{155} \approx 1.709677$, then $113.75 \times 1.709677 \approx 194.48$

Answer:

$194.48$ m