In order to avoid a storm a pilot starts the flight 13 degrees off course. After flying 80 miles in this direction the pilot turns the plane to head toward the destination. The angle formed by the course of the plane during the first part of the flight and the course during the second part of the flight is 160 degrees.
A) What is the distance of the flight?
B) Find the distance of a direct flight to the destination.
I don't know how to start or what the problem's supposed to look like.
A) What is the distance of the flight?
B) Find the distance of a direct flight to the destination.
I don't know how to start or what the problem's supposed to look like.
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Okay, so hopefully I read this properly..
Draw a dot on a piece of paper. This is the starting point of the plane (call this point S). Now from that point, draw a straight line. This is the path the plane is supposed to take. Now go back to point S and draw a line tilting up from it. This is the path the plane actually takes. Your picture should look something like this:
http://thesaurus.maths.org/mmkb/entry.ht…
The straight line is the normal course, but the tilted line is the course the pilot takes. The pink shading indicating the size of the angle is 13 degrees. Got that? Now at a certain point, the pilot switches back, right? Well draw a line from the tilted line (like in the picture) back down to the original line that represents the normal path. You'll get a triangle that looks sorta like this:
http://etc.usf.edu/clipart/38500/38596/t…
The leftmost angle is 13 degrees, and the top angle is 160 degrees. That means the angle on the right is 180-13-160, since all the angles in a triangle add up to 180 degrees. This is 7degrees,
Okay, now draw a line from the top most vertex of the triangle down to the base of the triangle. It will look something like Fig. 13 on the link below. Ignore the labelling there, just look at the way they split up the triangle by drawing that line from the top vertex:
http://chestofbooks.com/architecture/Bui…
Nowthe angle where that line meets the bottom line of the triangle is 90 degrees. That means you split the old triangle into two triangles. The left triangle has the angles: 13degrees (that you knew), 90 degrees (where the bisecting line meets the base), and the top angle is then 180-90-13 = 77degrees.
Draw a dot on a piece of paper. This is the starting point of the plane (call this point S). Now from that point, draw a straight line. This is the path the plane is supposed to take. Now go back to point S and draw a line tilting up from it. This is the path the plane actually takes. Your picture should look something like this:
http://thesaurus.maths.org/mmkb/entry.ht…
The straight line is the normal course, but the tilted line is the course the pilot takes. The pink shading indicating the size of the angle is 13 degrees. Got that? Now at a certain point, the pilot switches back, right? Well draw a line from the tilted line (like in the picture) back down to the original line that represents the normal path. You'll get a triangle that looks sorta like this:
http://etc.usf.edu/clipart/38500/38596/t…
The leftmost angle is 13 degrees, and the top angle is 160 degrees. That means the angle on the right is 180-13-160, since all the angles in a triangle add up to 180 degrees. This is 7degrees,
Okay, now draw a line from the top most vertex of the triangle down to the base of the triangle. It will look something like Fig. 13 on the link below. Ignore the labelling there, just look at the way they split up the triangle by drawing that line from the top vertex:
http://chestofbooks.com/architecture/Bui…
Nowthe angle where that line meets the bottom line of the triangle is 90 degrees. That means you split the old triangle into two triangles. The left triangle has the angles: 13degrees (that you knew), 90 degrees (where the bisecting line meets the base), and the top angle is then 180-90-13 = 77degrees.
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