Round answer to two significant digits.

An airplane flew 300 miles at a bearing of N65°E from airport A to airport B. The plane then flew at a bearing of S38°E to airport C. Find the distance from A to C if the bearing from airport A to airport C is S60°E.

Looks like a bit of "home-work " dumping here

I have done 2 of them for you,
you have shown no indication of any of your own work.
You try this one.

hint: make a diagram to show triangle ABC
All the angles in the triangle can be found, and you know one side AB = 300
Use the sine law.

Reiny, sorry I can't post the illustration

I know, I was able to do my diagram.

I want YOU to try it, let me know what you get

And I will find only the solution actually and I not prefer in the diagram

To find the distance from airport A to C, we need to break down the problem into two parts: the distance from A to B, and the distance from B to C.

First, let's find the distance from A to B. We can represent the bearing N65°E as a vector in the x-y coordinate plane.

N65°E can be split into two components: one in the north direction and one in the east direction.

The north component can be found using sine: sin(65°) = north component / 300 miles. Rearranging the equation, we find: north component = 300 miles * sin(65°).

Similarly, the east component can be found using cosine: cos(65°) = east component / 300 miles. Rearranging the equation, we find: east component = 300 miles * cos(65°).

Now, let's find the distance from B to C. We can represent the bearing S38°E as a vector in the x-y coordinate plane.

The south component can be found using sine: sin(38°) = south component / distance ABC. Rearranging the equation, we find: south component = distance ABC * sin(38°).

Similarly, the east component can be found using cosine: cos(38°) = east component / distance ABC. Rearranging the equation, we find: east component = distance ABC * cos(38°).

Now, let's find the total east and north components by adding up the values from A to B and from B to C:

Total east component = east component (from A to B) + east component (from B to C).
Total north component = north component (from A to B) + south component (from B to C).

To find the distance ABC, we can use the Pythagorean theorem:
distance ABC = square root of ((total east component)^2 + (total north component)^2).

Now let's calculate the values.

North component (from A to B) = 300 miles * sin(65°).
East component (from A to B) = 300 miles * cos(65°).
South component (from B to C) = distance ABC * sin(38°).
East component (from B to C) = distance ABC * cos(38°).

Total east component = East component (from A to B) + East component (from B to C).
Total north component = North component (from A to B) + South component (from B to C).

Now, we can apply the Pythagorean theorem:
distance ABC = square root of ((Total east component)^2 + (Total north component)^2).

Finally, round the answer to two significant digits.