Question

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

Answer 1

use the Cosine Rule:

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

x = 21.6

B is the correcct answer

Answer 2

Option B.

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=√(465.8656)`

`b=21.5839`

`b\approx 21.6`

Therefore, the correct option is B.