Question

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees tothe right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 635mi/h, how far is she from her starting position?Your answer ismi

Answer 1

Let's first make a diagram of the problem:

What we must find is the value of the line that is shown in green. For this we can first find the other two measures of the triangle, like this:

`635(mi)/(h)\cdot1.5h=952.5\text{ mi}`

And

`635(mi)/(h)\cdot2=1270\text{ mi}`

Since we have the measures of two of the sides and the angle opposite the one we want to find, we can use the cosine theorem:

`a^2=952.5^2+1270^2-2(952.5)(1270)\cdot\cos (170_{})`
`a=2214.22\text{ mi}`

She is 2214.22 miles far from the starting point.