Geographic directions are described in degrees, counting clockwise from a line going due north. Thus, for example, due north is zero degrees, east is 90 degrees, and southwest is 225 degrees.
All distances in this question are measured horizontally as you would measure them on a map. You can also think of flying at the altitude of the peak in question, instead of driving along the highway. The direction in which you see the peak is called its bearing. So a bearing of 135 degrees means it's southeast of you. Enter your answers as mathematical expressions (recommended) or as decimal approximations with at least 4 digits total.
You are driving at a constant speed of sixty miles per hour along a straight road going north. You see a prominent peak at a bearing of 45 degrees, and you know that that peak is 10 miles east of the road. At this time your distance from the peak is miles. Five minutes later you see the peak at a bearing of degrees. After another five minutes the peak is due east of you. At that precise spot there is a historical marker that tells you about the peak. 7 minutes after you pass the marker the peak is at a bearing of degrees. You sit back in your car and reflect on the pleasant fact that the trigonometry class you are taking makes it possible for you to figure out that $t$ minutes after you pass the historical marker the bearing of the peak is degrees. (Enter a mathematical expression involving the variable $t$.)
Hint: Draw a picture. Think of the Pythagorean Theorem. 60 miles per hour means a mile a minute. For the last two parts of this problem think of the angle you need to add to 90 degrees to get the bearing of the peak. You will need to use an inverse trig function. Remember that in WeBWorK the inverse trig functions return an angle measured in radians. You will need to convert it to degrees.