# Trigonometric bearing airplane problem

• Nov 13th 2011, 07:20 PM
hubbabubba590
Trigonometric bearing airplane problem
A plane's air speed is 520 mi/hr. Find the bearing (theta) the plane should fly to get to Seattle and the new speed (r) when the wind is blowing from a bearing of 120degrees with a speed of 120 mi/hr. The bearing from Hawaii to Seattle is 50 degrees and the distance is 2677 mi. Find the time it takes to fly to Seattle with the new plane speed.
• Nov 13th 2011, 07:22 PM
pickslides
Re: HELP! Trigonometric bearing airplane problem
Have you any ideas on what method to use?

Start by drawing a picture of the scenario described.
• Nov 13th 2011, 08:03 PM
Soroban
Re: HELP! Trigonometric bearing airplane problem
Hello, hubbabubba590!

I have a question . . .

Quote:

A plane's air speed is 520 mph.
Find the bearing (theta) the plane should fly to get to Seattle and the new speed (r)
when the wind is blowing from a bearing of 120 degrees with a speed of 120 mph.
The bearing from Hawaii to Seattle is 50 degrees and the distance is 2677 miles.
Find the time it takes to fly to Seattle with the new plane speed.

What "new speed"?

With the given data, we have a 'normal' bearing problem.

Code:

                        |                       S| 120d       N                *       |              *    *       |            *  110d  *       |      2677 *              *       |        *                  * A       |      *              *       |    *          *       |50d*      *       | *  *     H *
The plane flies from $H$ to $A$ at 520 mph.
The wind blows from $A$ to $S$ at 120 mph.

We can find the bearing $(\angle N\!H\!A)$ and the distance $\overline{HA}.$

What purpose does the "new speed" serve?

• Nov 13th 2011, 08:21 PM
hubbabubba590
Re: HELP! Trigonometric bearing airplane problem
Perhaps it's because the speed and direction of the wind causes the plane to slow down? I'm not quite sure, it's a practice problem my trigonometry teacher gave us. We are currently studying the applications of vectors in the plane.
• Nov 13th 2011, 08:23 PM
pickslides
Re: HELP! Trigonometric bearing airplane problem
Was there any other pieces of information?
• Nov 13th 2011, 08:36 PM
hubbabubba590
Re: HELP! Trigonometric bearing airplane problem
the attatchment is a similar problem with different speeds for the air plane and wind, this is how my teacher wants us to solve it