Homework Help: trig

Posted by Anonymous on Thursday, May 26, 2011 at 10:28am.

A plane is flying 225 mph heading South 25°West. The wind is blowing South 80°East at 60 mph.

What is the bearing of the plane?
What is the smallest angle of the triangle?
What is the largest angle of the triangle?
What is the remaining angle of the triangle?
What is the ground speed of the plane?

trig - Henry, Saturday, May 28, 2011 at 11:43am
Vp=225mi/h@(270-25) + 60mi/h@(270+80).
Vp = 225mi/h@245deg + 60mi/h@350deg.
Vp=(225cos245+60cos350) +
i(225sin245+60sin350).

Vp = (-95.1+59.1) + i(-203.9-10.4),
Vp = -36 - i214.3,

1. tan(Ar) = -214.3 / -36 = 5.95,
Ar = 80.5deg.
A = Ar + 180 = 80.5 + 180 = 260.5deg. =
Direction(bearing).

2. 90 - Ar = 90 - 80.5 = 9.5deg. = smallest angle.

3. 90deg = Largest angle.

4. 90 - 9.5 = 80.5deg.

5. Vp^2 = (-36)^2 + (214.3)^2 = 47,220.49,
Vp = 217.3mi/h.

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