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2 years ago

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Mathematics

1 answer:

Triss [41]2 years ago

4 0

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.

<h3>What are Similar Triangles?</h3>

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.

Learn more about similar triangles on:

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