Question

an engineer decides to use similar triangles to find the distance across the river she makes the diagram below which triangles to conclude that they are similar

Answer 1

Explanation:

The missing diagram is shown below. Remember that shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. So this means you can make the object bigger or smaller. So in this case, we know that ΔABC is similar to ΔDEF. If so, we can establish the following proportion:

$\frac{h}{56.7}=\frac{17.2}{52.4} \\ \\ h=56.7\times \frac{17.2}{52.4} \\ \\ h=18.61m$

Our goal is to find x. So by Pythagorean theorem:

$x=\sqrt{17.2^2+18.61^2} \\ \\ \boxed{x=25.34m}$

Conclusion:

ΔABC ~ΔDEF

Distance across the river is 25.34m