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A ship travels 12 miles from point A to point B, makes a turn of 112 degrees, and travels 14 miles to point C. If the ship travels directly from point C back to Point A, how many miles will it travel on the last leg of the trip(from point C to point A)? Round your answer to the nearest tenth of a mile.


A)23.4 miles

B)21.6 miles

C)16.2 miles

D)18.8 miles

Verified Answer :

use the Cosine Rule:

x^2 = 12^2 + 14^2 - 21214 cos 112

x =  21.6

B is the correcct answer

Answer:

Option B.

Step-by-step explanation:

Given information: AB=12 miles, BC=14 miles and ∠B=112°.

Using given information, we get

\(AB=c=12\text{ miles}\)

\(BC=a=14\text{ miles}\)

We need to find the value of CA or b.

Cosine formula:

\(b^2=a^2+c^-2ac\cos B\)

Substitute a=14, c=12 and B=112.

\(b^2=(14)^2+(12)^-2(14)(12)\cos (112)\)

\(b^2=196+144-336(-0.3746)\)

\(b^2=340+125.8656\)

\(b^2=465.8656\)

Taking square root on both sides.

\(b=\sqrt{465.8656}\)

\(b=21.5839\)

\(b\approx 21.6\)

Therefore, the correct option is B.

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