Question

---------50 POINTS PLEASE HELP-------

Answer 1

Answer:

(a). Two  triangles are similar

(b). Width of river approx 145.5 ft

Step-by-step explanation:

Answer 2

Answer:

$(a).\ Two\ triangles\ are\ similar\\\\(b).\ Width\ of\ river\approx 145.5\ ft$

Step-by-step explanation:

(a): Similar Triangles(AA): If two angles of a triangle is equal to corresponding two angles of other triangle. The two triangles are similar.

$In\ the\ \triangle ABC\ and\ \triangle EDC\\\\\angle DCE=\angle BCA\ \ \ \ \ (opposite\ angles)\\\\\angle CDE=\angle CBA\ \ \ \ \ (Right\ angles)\\\\Hence\ By\ AA\ Theorem\ These\ two\ triangles\ are\ similar$

(b):

$\triangle ABC\ and\ \triangle EDC\ are\ similar\\\\\frac{AB}{DE}=\frac{BC}{CD}\\\\BC=100\ ft,\ CD=22\ ft,\ DE=32\ ft\\\\\frac{AB}{32}=\frac{100}{22}\\\\AB=\frac{100}{22}\times 32\ \ \ \ \ \ \ \ Multiplying\ both\ sides\ by\ 32\\\\AB=\frac{3200}{22}\\\\AB=145.45\ ft\approx 145.5\ ft$