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 Post subject: direction of an airplanePosted: Sat, 14 Oct 2006 23:48:15 UTC
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Joined: Tue, 14 Mar 2006 02:41:28 UTC
Posts: 45
An airplane whose air speed is 620 km/h is supposed to fly in a straight path 35.0 degree north of east. But a steady 95 km/h wind is blowing from the north. In what direction should the plane head?

Here is what I thought:
direction of the plane

after rearranging:

then how do you solve for theta?
is there a better way to do it?

Last edited by xibaryon on Tue, 1 Feb 2011 15:10:09 UTC, edited 3 times in total.

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 Post subject: Re: an airplanePosted: Sun, 15 Oct 2006 00:59:28 UTC
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Joined: Sat, 14 Jan 2006 22:40:49 UTC
Posts: 694
Location: Yountville, California
xibaryon wrote:
An airplane whose air speed is 620 km/h is supposed to fly in a straight path 35.0 degree north of east. But a steady 95 km/h wind is blowing from the north. In what direction should the plane head?

Here is what I thought:
direction of the plane

after rearranging:

then how do you solve for theta?
is there a better way to do it?

Here's how to solve your equation. But it does suggest there may be a better way to set up the problem to make it easier to solve.

Write your equation as

then

Let and Use the second of these trig identities

to get

and

If anyone knows of a good web page describing this method, please let me know. The method is called introducing an auxiliary angle.

Last edited by Bilbo on Mon, 28 Feb 2011 04:56:56 UTC, edited 1 time in total.

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 Post subject: Posted: Mon, 16 Oct 2006 23:10:25 UTC
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Joined: Wed, 19 May 2004 22:26:01 UTC
Posts: 553
Let angle A be the increase adjustment in direction North of East. Then

SinA = 95sin125/620

A = 7.21 deg

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 Post subject: Posted: Wed, 18 Oct 2006 02:38:21 UTC
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Joined: Tue, 14 Mar 2006 02:41:28 UTC
Posts: 45
bowery boy wrote:
Let angle A be the increase adjustment in direction North of East. Then

remember i am trying to find a better way to solve it than what i have.

can you elaborate a bit more?

Last edited by xibaryon on Tue, 1 Feb 2011 15:10:34 UTC, edited 2 times in total.

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 Post subject: Posted: Thu, 19 Oct 2006 13:44:56 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 14 Jan 2006 22:40:49 UTC
Posts: 694
Location: Yountville, California
bowery boy wrote:
Let angle A be the increase adjustment in direction North of East. Then

SinA = 95sin125/620

A = 7.21 deg

Using the Law of Sines is slick.

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