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.