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Gilligan sees a ship coming close to the shore he’s standing on.

he wants to determine the distance (segment SD) from the ship to the shore.

he walks 130ft along the shore from point D to point C and marks the spot.

then he walks 23ft further and marks point B.

he turns 90° and walks until his location (point A), point C, and point S are collinear.

Answer the following questions making sure to show all your work.

(A) can Gilligan conclude that triangle ABC and triangle SDC are similar? why or why not?

(B) suppose AB = 150ft. what is the distance from the ship to the shore? show all your work and round your final answer to the nearest tenth of a foot.

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akposevictor akposevictor · Answer 1 · 2022-02-24T13:16:03+01:00

a. Based on the AA similarity theorem, Gilligan can conclude that, ΔABC ~ ΔSDC.

b. To the nearest tenth of a foot, the distance from the ship to the shore is: 847.8 ft.

The ratios of the corresponding sides of two triangles that are similar are equal.

Two triangles with two pairs of congruent angles are similar to each other based on the AA similarity theorem.

a. In ΔABC and ΔSDC, there are two pairs of congruent angles - ∠DCS ≅ ∠BCA (vertical angles) and ∠ABC ≅ ∠SDC (right angles)

Therefore, based on the AA similarity theorem, Gilligan can conclude that, ΔABC ~ ΔSDC.

b. AB = 150 ft

Distance from the ship to the shore = SD = ?

DC = 130 ft

CB = 23 ft

Thus:

AB/SD = CB/DC

Substitute

150/SD = 23/130

SD = (150×130)/23

SD = 847.8

Thus, to the nearest tenth of a foot, the distance from the ship to the shore is: 847.8 ft.

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