I didn't think you could... maybe I'm interpreting the question wrong. You have to picture the triangle the flight path makes... here's the q:
"You start your first in-flight navigation lesson by taking off from an airport at point A. You fly one hour north and 110 mph and reach point T. You turn 60 degrees to the right (east) and fly for another hour at the same speed and reach point G. Your instructor says to aim the plane back to the airport to form a triangular flight path. In order to do this, you must calculate angle G. Use sine law to determine the angle, to the nearest degreee, to set the course on. Include a diagram of your triangular flight path and find all the interior angles."
So the triangle I came up with had two sides of 110 miles in length (heading north and heading east) and an angle between those sides that measured 60 degrees. So I can't use the sine law because I don't have the measure of the side opposite T (the 60 degree angle). What am I doing wrong or am I right?
"You start your first in-flight navigation lesson by taking off from an airport at point A. You fly one hour north and 110 mph and reach point T. You turn 60 degrees to the right (east) and fly for another hour at the same speed and reach point G. Your instructor says to aim the plane back to the airport to form a triangular flight path. In order to do this, you must calculate angle G. Use sine law to determine the angle, to the nearest degreee, to set the course on. Include a diagram of your triangular flight path and find all the interior angles."
So the triangle I came up with had two sides of 110 miles in length (heading north and heading east) and an angle between those sides that measured 60 degrees. So I can't use the sine law because I don't have the measure of the side opposite T (the 60 degree angle). What am I doing wrong or am I right?
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the angle T (angle between segments AT and TG) is not 60 degrees, the problem says you have a 60 degree angle between the vertical (line AT), and segment TG. The angle T is 180 - 60 degrees = 120 degrees. Please draw a clear picture to understand this. When it says you turn 60 degrees east, it was in reference to the direction you were going in originally (north).
You are making the most common problem students have at first with geometry: not being able to think beyond a one-step solution. I like to tell students that if they are stuck, to think about the end. What would be the final step to get the angle G?
law of sines: sin(G) / AT = sin(T) / AG ---> G = sin^{-1} [ (AT/AG) sin(T)]
right? That will give you the angle G.
so in that equation, you know AT = 110 miles, and you know T = 120 degrees. All you need to know is AG and you are done.
How can you find AG? Originally all you know is AT, TG, and angle T. In other words, you have two side lengths, one angle and you need another side length. This is exactly the prescription needed for the law of cosines (to find AG). Can you take it from here?
You are making the most common problem students have at first with geometry: not being able to think beyond a one-step solution. I like to tell students that if they are stuck, to think about the end. What would be the final step to get the angle G?
law of sines: sin(G) / AT = sin(T) / AG ---> G = sin^{-1} [ (AT/AG) sin(T)]
right? That will give you the angle G.
so in that equation, you know AT = 110 miles, and you know T = 120 degrees. All you need to know is AG and you are done.
How can you find AG? Originally all you know is AT, TG, and angle T. In other words, you have two side lengths, one angle and you need another side length. This is exactly the prescription needed for the law of cosines (to find AG). Can you take it from here?