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?

Please help me out, thank you. <3

Certainly! Let's go through each question step by step.

6. To find the ground speed of the plane, we need to consider the effect of the wind on the plane's motion. The ground speed is the actual speed of the plane relative to the ground. To calculate it, we can use vector addition.

First, we decompose the velocity of the plane and the wind into their respective north-south and east-west components. The velocity of the plane is 240 mph at an angle of N60°E, so its north-south component would be 240 * cos(60°) and its east-west component would be 240 * sin(60°).

Similarly, the wind is blowing at 30 mph at an angle of S30°E, so its north-south component would be -30 * cos(30°) and its east-west component would be 30 * sin(30°).

Now, we add the respective components of the plane and the wind to get the net velocity components. The north-south net velocity component is (240 * cos(60°)) + (-30 * cos(30°)) and the east-west net velocity component is (240 * sin(60°)) + (30 * sin(30°)).

Finally, we use the Pythagorean theorem to find the magnitude of the net velocity, which is the ground speed of the plane:

Ground speed = sqrt((north-south net velocity component)^2 + (east-west net velocity component)^2)

Plugging in the values, we get the ground speed of the plane.

7. To find the smallest angle in the triangle, we need to determine the angle opposite the smallest side which can be calculated using the Law of Cosines. The smallest side is the wind speed, which is 30 mph. We also need to know the lengths of the other two sides of the triangle, which are the north-south and east-west net velocity components we calculated earlier. Using the Law of Cosines, we can solve for the smallest angle.

8. Similarly, to find the biggest angle in the triangle, we need to determine the angle opposite the largest side. In this case, the largest side is the ground speed of the plane. We can use the Law of Cosines again to find the largest angle.

9. To find the remaining angle in the triangle, we can subtract the sum of the smallest and largest angles from 180 degrees. This is because the sum of all angles in a triangle is always 180 degrees.

10. The bearing of the plane refers to the direction of the plane's motion relative to a fixed point, usually referenced by the four cardinal directions (north, south, east, and west). To find the bearing, we need to combine the angle of the plane's motion, N60°E, with the wind direction, S30°E. We can use trigonometry and vector addition to find the resulting angle.

I hope this explanation helps you find the answers to your questions!