Time Lost Due to Navigation Error

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greatwhiteshark

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In attempting to fly from city A to city B, an plane followed a course that was 10 degrees in error. After flying a distance of 50 miles, the pilot corrected the course by turning at point C and flying 70 miles further. If the constant speed of the plane was 250 miles per hour, how much time was lost due to the error?

What formula can I use to find the answer? I don't want the answer. I just want you to help me set up the proper equation that will help me find the answer on my own.
 
Have you taken a peek at the Law of Sines? Careful, though, it won't give you the obtuse angle you need.

That was a lot of homework. Thank you VERY MUCH for showing your work. Try to be more descriptive.
 
How can you use the law of sines and get no answer? That makes no sense.

Draw a picture.

Draw a line segment.
Label one end S, the beginning of the trip.
Label the other end E, the end of the trip.
Draw another line segment, heading off to the left or right just a little, make it about half as long as segment SE.
Label the end point T, the turning point.
Draw another segment from T to E.

We are given:
Segment ST is 50 miles.
Segment TE is 70 miles.
Angle EST is 10 degrees.

Recognize the situation of two sides and the angle NOT between them. This could be a problem. However, since the side opposite the known angle is longer than the side adjecent to the known angle, we have no difficulty. If it works, there is only one answer. (I didn't think about this long enough when I suggested there may be a problem with an obtuse angle, above.)

Label side SE, c, the intended trip length.
Label angle SET, A.
Lbel angle STE, C.

Using the Law of Sines, which ALWAYS gives an answer:

70/sin(10º) = 50/sin(A)

Solving for A, gives A = 7.125º
Solving for C, gives C = 180º - 10º - 7.125º = 162.875º

Using the Law of Cosines, which ALWAYS gives an answer:

c<sup>2</sup> = 50<sup>2</sup> + 70<sup>2</sup> - 2*50*70*cos(162.875º)

Solving for c, gives c = 118.7 miles - The length of the intended trip.

We're not done. Now, you answer what the question wants.
 
okay

I did not know that the law of cosines could also be applied here. Okay....I will go forward with this question on my own. I'm sure it is not hard.
 
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