Question

Use the image to answer the question.

Two sailboats, labeled A and B, are oriented diagonally. Each sailboat features a triangular sail, a hull, and a mast connecting them.

△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

25 miles
25 miles

28 miles
28 miles

12 miles
12 miles

14 miles
14 miles
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Answer 1

Because C is the midpoint of AE, AC = AE/2 = 30/2 = 15. From the picture triangles ABC and EDC are right triangles with the right angle at B (and D), so in triangle ABC AC is the hypotenuse.

Thus BC = sqrt(AC^2 − AB^2) = sqrt(15^2 − 5^2) = sqrt(225 − 25) = sqrt(200) = 10√2 ≈ 14.142.

Since C is the midpoint of DB, DB = 2·BC ≈ 2·14.142 ≈ 28.284, so to the nearest mile DB = 28 miles.