Question

Island a is 230 miles from island b. a ship captain travels 260 miles from island a and then finds that he is off course and 200 miles from island b. what bearing should he turn to, so he is heading straight towards island b?

Answer 1

The measure of angle C comes out to be 58.267 degrees.

According to the statement

we have to find that the angle at which the boat is turned.

So, For this purpose, we know that the

And the given information is a visualized with the diagram.

For this please see the image below.

So,

We have 3 sides of the triangle ABC, using the measure of these sides we can find the angle opposite to side c which will help us in finding the measure of bearing.

And

Law of cosine relates the 3 sides of the triangle and angle opposite to one side by following equation:

$A^{2} +B^{2} - 2AB Cos(C) = C^{2}$

Substitute the values in it then

A= 200, B = 260, C = 230

Using the values of a,b, and c we get:

$200^{2} +260^{2} - 2(200)(260) Cos(C) = 230^{2}$

$200^{2} +260^{2} - 230^{2} = 2(200)(260) Cos(C)$

Then after solving it become

$Cos(C) = \frac{200^{2} +260^{2} - 230^{2} }{2(200)(260)}$

$Cos(C) = \frac{547}{1040}$

And then

C = 58.267

Thus, the measure of angle C comes out to be 58.267 degrees. The angle with which the boat will have to turn will be:

180 - 58.267 = 121.733 degrees.

So, The measure of angle C comes out to be 58.267 degrees.

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