Question

Find distance A-B plz help! picture attached

Answer 1

Answer:

Step-by-step explanation:

The triangles are set up so we see that angle A and angle D are congruent.  We also know that, by the definition of vertical angles, angles CED and BEA are congruent.  That means, by the Triangle Angle-Sum Theorem, that angles C and B are also congruent.  That does NOT mean, however, that the triangles are congruent because their corresponding side lengths are not the same.  What it does mean is that the triangles are similar.  If we were to pull them apart and set them next to each other, our triangle similarity statement would be that ΔECD ~ ΔEBA.  That means that their corresponding sides exist in proportion to one another.  Namely, side ED is proportional to side EA, and side CD is proportional to side BA.  That's all we need to find the length of BA, the distance across the lake. The proportion is set up like this:

$\frac{ED}{EA}=\frac{CD}{BA}$  and fill in the distances:

$\frac{400}{2100} =\frac{200}{BA}$

Cross multiply to solve for BA:

400BA = 420000 so

BA = 1050 feet