Two pilots take off from the same airport. Mason heads due south. Nancy heads 23º west of south. After 400 land miles, how far is Nancy from Mason’s route? Round your answer to the nearest tenth of a mile. (Enter only the number.)(If someone had helped me with the one similar to this I probably wouldn't be asking)
Draw a diagram. Draw a line S for Mason.
Draw a line 400 long at S 23° W for Nancy. Draw a line directly east so connect the end of Nancy's route to Mason's line. That line will be of length x, such that
x/400 = sin 23° = 0.39
So, x = 156.3 mi from Mason's course.
To find out how far Nancy is from Mason's route, we need to first find out their respective positions after traveling 400 land miles.
Since Mason heads due south, he would be 400 miles directly south of the airport. This forms a triangle where one side is the distance traveled by Mason.
For Nancy, who heads 23º west of south, we need to calculate the southward distance traveled and then calculate the westward distance traveled at that point.
Given that Nancy traveled 400 miles, the southward distance traveled can be calculated by taking the sine of 23º and multiplying it by 400:
Southward distance = sin(23º) * 400
Now, to find the westward distance, we can take the cosine of 23º and multiply it by the southward distance:
Westward distance = cos(23º) * (sin(23º) * 400)
To find the distance Nancy is from Mason's route, we can use the Pythagorean theorem since we have the southward and westward distances as the two sides of a right triangle:
Distance from Mason's route = sqrt((westward distance)^2 + (southward distance)^2)
Substituting the values we calculated:
Distance from Mason's route = sqrt((cos(23º) * (sin(23º) * 400))^2 + (sin(23º) * 400)^2)
Evaluating this expression will give us the distance from Mason's route.