Question

a pilot flies in a straight path for 1 h 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. if she maintains a constant speed of 665 mi/h, how far is she from her starting position?
your answer is
mi;
enter your answer rounded to two decimal places.
question help:
worked example 1

Explanation:

Step1: Calculate the lengths of the two sides of the triangle

• First, convert the time to hours. \(1\) hour \(30\) minutes \(= 1.5\) hours.
• Using the formula \(d = vt\) (where \(d\) is distance, \(v\) is speed, and \(t\) is time), for the first - part of the journey: \(a=665\times1.5 = 997.5\) miles.
• For the second - part of the journey: \(b = 665\times2=1330\) miles.
• The included angle \(\theta=180^{\circ}- 10^{\circ}=170^{\circ}\)

Step2: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\).
Substitute \(a = 997.5\), \(b = 1330\), and \(\theta = 170^{\circ}\) (\(\cos(170^{\circ})\approx - 0.9848\)) into the formula:

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Answer:

\(2319.58\)