(This question is all about bearings and trigonomentry).
A helicopter has flown from its base on a bearing of 153 degrees. Its distance east of base is 19km. How far has the helicopter flown?
2007-11-22 06:27:29 · 3 answers · asked by Salsa034848 2 in Science & Mathematics ➔ Mathematics
Ok, here we go. Put a dot on a piece of paper and call this 'base'. If (don't actually do this) you were to draw a line vertically upwards from this point, that would be north which is 0 deg. Equally, if you were to draw a line vertically downwards from 'base', this would be south which would be 180 deg. So you can see that a bearing of 153 deg would be down from base and slightly to the right because it's less than 180 deg. Draw this line in now. It doesn't have to be accurate it's just to help you form a picture of the situation. If you now draw a line horizontally from base out to the right, this would be east. Finally, and to complete the picture, draw a line vertically upwards from the end of the line representing 153 deg to the line representing east. Ignoring any points where lines cross-over, we should now have an upside-down right-angled triangle.
We know that the length of the horizontal line is 19km. We can also deduce that the angle from east to the bearing line is 63 deg 153 - 90. This gives us: cos 63 deg = 19/x (cos = adjacent over hypotenuse). Transposing this, we get x = 19/cos 63. Using your calculator, you should arrive at a figure of around 41.85km.
2007-11-22 07:16:49 · answer #1 · answered by brainyandy 6 · 2⤊ 0⤋
Draw a right angle triangle with a base of length 19 and an angle of 63 degrees (153 - 90, since bearings are all made from the north) between the base and the hypotenuse.
The problem has now been transformed to finding the length of the hypotenuse, H.
H = 19/cos(63) = 41.85 km
2007-11-22 14:59:16 · answer #2 · answered by perplexed* 3 · 1⤊ 0⤋
draw the triangle.
sin 27 = 19/d
d = 19 / sin27 = 41.85
2007-11-22 15:01:59 · answer #3 · answered by norman 7 · 0⤊ 0⤋