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?

Please help out with these questions, thank you. <3

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?
I am lost on these

11. The bearing of the plane can be found by subtracting the wind's direction from the plane's heading. In this case, the plane is heading S25°W, and the wind is blowing S80°E. So, if we add the two directions together, we get S25°W + S80°E = S25°W - N10°E. Voilà!

12. Well, since we know the plane is flying southwest, that forms a right triangle when combined with the wind's direction. The smallest angle in a right triangle is always 90 degrees. So, there you have it!

13. The largest angle in a triangle is always opposite the longest side. If we assume the wind speed is the longest side, then the largest angle in the triangle would be opposite to it.

14. The remaining angle of a triangle can be found by subtracting the sum of the other two angles from 180 degrees. So, you just need to subtract the smallest and largest angles from 180 degrees to find the remaining angle.

15. To find the ground speed, we need to combine the plane's speed with the component of the wind that acts in the direction of the plane's heading. We can do this using vector addition. Since it's a right triangle, we can use the trigonometric functions to find the component of the wind's speed that acts in the direction of the plane's heading. Once we have that, we can add it to the plane's speed to get the ground speed.

16. Well, to find 2A - B, we need to multiply vector A by 2 and then subtract vector B from it. So, if vector A has a magnitude of 3 in the leftward direction, multiplying it by 2 would give us a magnitude of 6. And since vector B has a magnitude of 5 in the rightward direction, we can subtract it from 2A and get the final result.

To solve these questions, we will use vector addition and trigonometry. Let's go through each question one by one:

11. To find the bearing of the plane, we need to determine the resultant direction of the plane's velocity and wind velocity. We can achieve this by adding these two vectors.

The plane's velocity can be represented by a vector with magnitude 225 mph and direction S25°W. To convert this direction into components, we can break it into its southward and westward components. Since the angle is measured clockwise from the south, the southward component will be (225 mph) * sin(25°), and the westward component will be (225 mph) * cos(25°).

The wind velocity can be represented by a vector with magnitude 60 mph and direction S80°E. To convert this direction into components, we can break it into its southward and eastward components. Since the angle is measured clockwise from the south, the southward component will be (60 mph) * sin(80°), and the eastward component will be (60 mph) * cos(80°).

To find the resultant direction, we need to add the southward and eastward components together, and then find the angle that this resultant vector makes with the south direction. We can use trigonometry to find this angle.

After finding the angle, we can convert it into bearing notation. Bearing is measured clockwise from the north, so the bearing will be 360° minus the angle we found.

12. To find the smallest angle of the triangle, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angles A, B, and C respectively, the following equation holds: c^2 = a^2 + b^2 - 2ab * cos(C). Since we have all the side lengths of the triangle, we can plug them into this equation to find the smallest angle.

13. To find the largest angle of the triangle, we can use the Law of Cosines again. We can apply the equation c^2 = a^2 + b^2 - 2ab * cos(C), but this time c will be the longest side of the triangle.

14. To find the remaining angle of the triangle, we can subtract the sum of the two known angles from 180° (since the angles in a triangle add up to 180°).

15. To find the ground speed of the plane, we need to find the resultant velocity vector of the plane's velocity and wind velocity. We can achieve this by adding these two vectors using vector addition. The magnitude of the resultant vector will be the ground speed of the plane.

16. To find the value of 2A - B, we need to determine the direction and magnitude of vector A and B. Vector A has a magnitude of 3 in the leftward direction, so its components will be (-3, 0). Vector B has a magnitude of 5 in the rightward direction, so its components will be (5, 0). To find 2A - B, we can multiply the components of A by 2, subtract the components of B, and then calculate the magnitude of the resultant vector.

I did a very similar question like yours here

http://www.jiskha.com/display.cgi?id=1306326095

study the solution and apply it to your problem.