A plane leave a certain airport from runway 4 RIGHT, whose bearing is N40degreesE. After flying for 1/2 mile, the pilot requestd permission to trun 90 degrees and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the plane?
After my work, I got S23.4degreesE but the book's answer is
S76.6degreesE.
How do I get the book's answer? Why is my answer wrong?
let's give some letter names to our triangle
let the origin be O
let the end of the first leg be A, the end of the second leg be B
then OA=.5 and AB = 1 and angle A = 90º
so by Pythagoras OB = 1.118
and angle AOB = 63.4
so the plane is flying 103.43 from north
which when subtracted from 180 is 76.57º as your book says
To find the correct answer, you need to break down the problem into smaller steps and carefully consider the directions and angles involved.
1. Start from the initial runway direction: Runway 4 RIGHT, bearing N40°E. This means the runway is facing N40°E and the plane departs in that direction.
2. After flying for 1/2 mile, the pilot requests permission to turn 90° towards the southeast. This implies that the plane turns towards the right side by 90°.
3. To find the new bearing, you need to determine the angle formed between the plane's direction and the north. The original bearing was N40°E, and turning 90° to the right means the new angle would be N40°E + 90° = N130°E.
4. The plane then flies 1 mile in this new direction.
5. To find the final bearing, you need to determine the angle formed between the line connecting the starting point and the final position of the plane and the north direction.
6. Draw a diagram and label the starting point, midpoint (after flying 1/2 mile), and final position of the plane.
7. With the midpoint as the center, draw an arc with a radius of 1 mile to represent the distance traveled. This arc will intersect with the line connecting the starting point and midpoint.
8. Measure the angle formed between the north direction and the line connecting the starting point and the intersection point on the arc.
9. From the measured angle, you can determine the bearing by subtracting the angle from 90° and converting it to the appropriate notation (E or W). In this case, the angle should be S.
It's important to double-check your calculations and diagrams to ensure accuracy. If you got a different answer than what is provided in the book, it's likely due to a miscalculation or misinterpretation of the instructions. Review your steps and angles carefully to find any errors.