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.
Did you make your sketch?
Mine is triangle ABC with
angle A = 55°
angle C = 22°, and
angle B + 103°
then it is just a matter of the sine law:
AC/sin103 = 300/sin22
I got AC = appr 780 miles
The bearing of town P and Q is 315°, while town R is south of town P and west of town Q. if town R is 60km away from town Q, how far is town R to from town P
what an air craft is flying from certain airfield 15 degree north and 105 east to 15 north and 45 degree west calculate the distance moved by the plane.
To find the distance from Airport A to Airport C, we can break down the problem into two parts: finding the distance from Airport A to Airport B and finding the distance from Airport B to Airport C.
1. Distance from A to B:
The airplane flew 300 miles at a bearing of N65°E from Airport A to Airport B.
Let's define the North direction as 0° and the East direction as 90°.
Since the bearing is N65°E, we need to split it into North and East components.
The North component can be calculated using sine: sin(65°) = North component / 300 miles.
North component = sin(65°) * 300 miles.
Similarly, the East component can be calculated using cosine: cos(65°) = East component / 300 miles.
East component = cos(65°) * 300 miles.
2. Distance from B to C:
The airplane flew at a bearing of S38°E from Airport B to Airport C.
Similarly, we split the bearing into South and East components.
The South component can be calculated as: sin(38°) = South component / distance from B to C.
South component = sin(38°) * distance from B to C.
The East component can be calculated using cosine: cos(38°) = East component / distance from B to C.
East component = cos(38°) * distance from B to C.
Now, let's move on to finding the distance from Airport A to Airport C by using the information we have:
To find the total distance from A to C, we need to add the distances from A to B and from B to C.
The North component from A to B + the South component from B to C should add up to the South component from A to C.
Similarly, the East component from A to B + the East component from B to C should add up to the East component from A to C.
So, let's set up the equation:
sin(65°) * 300 miles + sin(38°) * distance from B to C = sin(60°) * distance from A to C.
Now, we can solve this equation to find the distance from Airport A to Airport C.