TRIGONOMETRY HELP PLEASE?
An airplane travels at 180 km/hr for 2 hours in a direction of 210degrees. At the end of this time, how far south of the airport is the airplane?
Note: Directions are given in degrees clockwise from north.
The airplane is ____ kilometers south of the airport after 2 hours?
- billrussell42Lv 72 months ago
210º is 30º S of N
180 km/hr x 2 hr = 360 km
d = 360 sin 30 = 360/2 = 180 km
- DWReadLv 72 months ago
2 hours × (180 km)/hour = 360 km
Draw a picture. The path of the airplane is the hypotenuse of a 30-60-90 triangle. The sides of a 30-60-90 triangle are in the ratio 1:√3:2.
The hypotenuse is 360 km, so the side opposite the 60° angle is 180√3 km ≅ 312 km.
The airplane is 312 km south of the airport.
- RaymondLv 72 months ago
Make a drawing (it does not have to be to scale - but it will help you understand). Make it look like an x-y plot (Cartesian grid). Leave more room below than above (the airplane is moving "down" on your graph).
At the origin (0, 0), put the airport.
Label the axes:
The positive (right) end of the x axis is 090 degrees (East)
The negative (bottom) end of the y axis is 180 degrees (South)
The negative (left) end of the x axis is 270 degrees (West)
The positive (top) end of the y axis is 360 degrees (in marine navigation, we use 000, but it means the same thing: due North)
210 is the direction that is 30 degrees "clockwise" from due South (180)
Draw a line in that direction.
The length of the line is 2 h times 180 km/h = 360 km
This length will become the hypotenuse of the triangle we will construct:
From the end of this line, draw a horizontal line that will hit the y-axis at a 90-degree angle. You now have a right-angle triangle formed by the hypotenuse, the y-axis and this perpendicular line you just added.
You are looking for the length along the y-axis (it is the north-south line - therefore it is on that line that you measure how far south you are).
It is adjacent to the angle (at the centre origin).
adjacent/hypotenuse = cosine
adjacent = cosine * hypotenuse = cos(210) * 360
If you do this directly on a calculator, you will see that the machine will automatically give you a negative value (cosine of 210 is a negative value). This will give you a negative value for the length of the adjacent side; when doing navigation problems in that fashion, a negative value for y means south.
I get a "southing" of around 312 km. I suggest that you write down the more precise value that you will get when you do it yourself.