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:
[tex]\frac{h}{56.7}=\frac{17.2}{52.4} \\ \\ h=56.7\times \frac{17.2}{52.4} \\ \\ h=18.61m[/tex]
Our goal is to find x. So by Pythagorean theorem:
[tex]x=\sqrt{17.2^2+18.61^2} \\ \\ \boxed{x=25.34m}[/tex]
Conclusion:
ΔABC ~ΔDEF
Distance across the river is 25.34m
