# geometry

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A plane is heading west at 200 mph. The wind is blowing S30°W at 25 mph.

1. What is the ground speed of the plane?

2. When you solve the triangle, what is the smallest angle?

3. What is the largest angle of the triangle?

4. What is the remaining angle?

5. What is the bearing of the plane?

A plane is is flying 240 mph heading N60°E. The wind is blowing S30°E at 30 mph.

6. What is ground speed of the plane?

7. What is the smallest angle in the triangle?

8. What is the biggest angle in the triangle?

9. What is the remaining angle in the triangle?

10. What is the bearing of the plane?

A plane is is flying 225 mph heading S25°W. The wind is blowing S80°E at 60 mph.

11. What is the bearing of the plane?

12. What is the smallest angle of the triangle?

13. What is the largest angle of the triangle?

14. What is the remaining angle of the triangle?

15. What is the ground speed of the plane?

16. Vector A has a magnitude of 3 in the leftward direction and B has a magnitude of 5 in the rightward direction. What is the value of 2A – B?

You can also answer other types of problems using vectors. Try this one:

Two forces are pushing on an object, one at 12 lbs of Force and one at 5.66 lbs of Force. The angle between them is 35° (each is 72.5 from horizontal, such that the forces make a v with the object in the center).

17. What is the total Force on the object?

18. What is the smallest angle of the triangle?

19. What is the largest angle in the triangle?

20. What is the remaining angle of the triangle?

• geometry -

I'll do a few, and you can use the method on the rest:

6. Draw the velocity triangle. The wind is blowing at right angles to the plane's air travel. So, you have a n air speed of 240 and a wind speed of 30, making the ground speed 30√65 = 241.87

7,8,9. The angles of the triangle are
smallest: arctan(1/8) = 7.125°
next: 90-7.125 = 88.875°
largest: 90°

10. Bearing is N67.125°E

• geometry -

oops. 90-7.125 = 82.875°

• geometry -

1. [S30oW] = 270-30 = 240o CCW.
Vpw = Vp + Vw = -200 + 25[240o] =
-200 + 25*Cos240 + i25*sin240 =
-200 - 12.5 - 21.7i = -212.5 - 21.7i =
-213.6[5.83o] = 213.6[185.83] CCW from
+X-axis. = [S84oW].

N60oE = 30o CCW from +X-axis.
S30oE = 300o CCW from +X-axis.

Vpw = Vp + Vw = 240[30o] + 30[300o] =
207.8 + 128i + 15 - 26i = 222.8 + 102i =
245mi/h[24.6o] CCW. = N65.4oE.

• geometry -

2. 6 Degrees.

3. 90 Degrees(84o= Largest acute angle)

4. 84 Degrees.

5. S84oW.

7. 24.6 Degrees.

8. 90 Degrees.

9. 65.4 Degrees.

10. N65.4oE.

11. S25oW = 245o CCW. S80E = 350o CCW.

Vpw = Vp + Vw=225[245o] + 60{350o] =
-95.1 - 204i + 59.1 - 10.4i = -36-214.4i
=-217.4[80.5o] = 217.4[80.5+180] =
217.4[260.5] CCW = 217.4mi/h[S9.5oW].

12. 9.5 Degrees.

13. 90 Degrees.

14. 90-9.5 = 80.5 Degrees.

15. 217.4 mi/h.

16. A = -3. B = 5.
2A - B = 2*(-3) - 5 = -11 = 11 Leftward.

17. F=F1 + F2 = 12[107.5o] + 5.66[72.5]=
12*Cos107.5 + i12*sin107.5 + 5.66*Cos72.5 + 5.66*sin72.5 =
-3.61 + 11.44i + 1.70 + 5.4i =
-1.91 + 16.9i =-17[-83.6o]=17[180-83.6]=
17Lbs[96.4o] CCW.= 17Lbs.[N6.4oW].

18. 6.4 Degrees.

19. 90 Degrees

20. 90-6.4 = 83.6 Degrees.

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