Question

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.

A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.

Law of cosines:

By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.

30 degrees
39 degrees
46 degrees
50 degrees

Answer 1

Answer:

Option B :39 degrees is the correct.

The nearest degree is 39°

Step-by-step explanation:

Laws of cosines relates each side with its opposite angle.

Formula for this is :

$c^{2} =a^{2} +b^{2} - 2abcosC$

$a^{2} = b^{2}+c^{2} - 2bccosA$

$b^{2} =a^{2}+c^{2} -2accosB$

in figure a=28

              b=18

              c=25

Here we have to find angle between a and c that is B

So $18^{2} = 25^{2} +28^{2} -2*25*28cosB$

324 = 625 + 784 - 1400cosB

1400cosB =  625 + 784 - 324

1400cosB = 1085

cosB = 0.775

∠B = 39.195° ≈ 39°

The boat change 39°  when it made its first turn.

Learn more about Laws of cosines here -https://brainly.ph/question/13424723

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