In attempting to fly from city P to city Q an aircraft followed a course that was 10 degrees in error,as indicated in the figure.After flying a distance of 50 miles ,the pilot corrected the course by turning at point R and flying 70 miles farther.If the constant speed of the aircraft was 250 miles per hour,how much time was lost due to the error
Answers
Given : In attempting to fly from city P to city Q an aircraft followed a course that was 10 degrees
After flying a distance of 50 miles ,the pilot corrected the course by turning at point R and flying 70 miles farther.
the constant speed of the aircraft was 250 miles per hour,
To Find : how much time was lost due to the error
Solution:
Distance covered = 50 + 70 = 120 miles
Straight Distance = a
Using cosine rule
=> cos 10° = ( a² + 50² - 70²) / 2a*50
=> 100acos10° = a² - 2400
=> a² - 98.48a - 2400 = 0
=> a = 118.7
( or it can be solved using sin rule )
sinA/a = sinB/b = SinC/c
Distance extra travelled = 120 - 118.7 = 1.3 miles
speed of the aircraft was 250 miles per hour
Time lost = 1.3 / 250 hrs
= 0.312 minutes
= 18.72 seconds
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