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:
brainly.com/question/11899908
Kilometres are not typically used because they are used to measure distances
I need help on this question too ugh
He made an error in step 1. Specifically, he distributed incorrectly.
The 3(x+2) portion is not the same as 3x+2. We need to multiply that '3' by the 2 as well to get 3*2 = 6
In other words, 3(x+2) should turn into 3x+6
If you wanted, you can think of 3(x+2) as three copies of (x+2) added together like this: (x+2)+(x+2)+(x+2) = (x+x+x)+(2+2+2) = 3x+6
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Check out the diagram below to see how his steps should look like. I basically started with what your teacher gave you, but changed a few things as shown in red.