Question

Two boats labeled A and B floating on a body of water. A diagonal dashed line extends from point A through point C to point E. Another boat is at point B, directly above point C, and a vertical dashed segment connects them. A horizontal dashed segment from D to E is also perpendicular to the vertical line, forming a right angle at D.


△ABC≅△EDC
and C
is the midpoint of AE¯¯¯¯¯¯¯¯
and DB¯¯¯¯¯¯¯¯
. If Boat A is 5 miles from Boat B, and Boat A is 30 miles from an object at point E
, then what is the length of DB¯¯¯¯¯¯¯¯
to the nearest mile?

(1 point)
Responses

14 miles
14 miles

28 miles
28 miles

25 miles
25 miles

12 miles

Answer 1

From ΔABC ≅ ΔEDC, ED = AB = 5 and DC = BC. C is midpoint of AE so EC = AC = 30/2 = 15. Triangle EDC is right at D, so

DC^2 + ED^2 = EC^2
DC^2 + 5^2 = 15^2
DC^2 = 225 − 25 = 200
DC = 10√2.

Since C is midpoint of DB, DB = 2·DC = 20√2 ≈ 28.28 ≈ 28 miles.

Answer: 28 miles.