On an x-y grid, label them N-S, E-W, draw a line from the origin to the right and label it 425 (you are going East)

From the end of that line draw a vertical line upwards of 40 (you are going North)

Use an approximate scale, realizing that 425 is just about 10 times "as long" as 40.
Join that endpoint to the origin.
This is your vector diagram and you should have a right-angled triangle where the hypotenuse is the magnitude.

The small angle at the origin will give you the direction angle of the plane.

A pilot heads his jet due east. The jet has a speed of 425mi/h relative to the air. The wind is blowing due north with a speed of 40mi/h. Find the direction of the jet. Confused about the angle. :( How do I sketch a diagram. Thanks a lot.

Thank you. But that is giving me the wrong answer.
From the diagram, tan(theta) = 40/425
so theta is 5.38.

The answer is 84.62, which I get when I use tan(theta) = 425/40
How is it possible? :(

we are both right, it all depends how you express the angle.

In navigation terms angles are stated clockwise from North.

the angle we have is 5.38 up from the "x-axis", which is 84.62 clockwise from North
(90 - 5.38 = 84.62)

To sketch the diagram, start by drawing the x-y grid and labeling the x-axis as East-West and the y-axis as North-South. The origin (0,0) represents the starting point.

To draw the line representing the jet's velocity relative to the air, start from the origin and draw a horizontal line to the right. Label this line as 425, representing the jet's speed in miles per hour (mph) going East.

From the end of that line, draw a vertical line upwards to represent the wind blowing due North. Label this line as 40, representing the wind's speed in mph blowing North.

Now, join the endpoint of the wind line to the origin to complete the vector diagram. This will form a right-angled triangle, with the hypotenuse representing the magnitude of the resultant velocity of the jet.

To find the direction angle of the plane, you can use the tangent function (tan). The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right-angled triangle.

In this case, the angle you want to find is the small angle at the origin. So you need to find the ratio of the vertical side (40) to the horizontal side (425) since tangent is equal to opposite/adjacent.

tan(theta) = 40/425

Solve for theta (angle):

theta = arctan(40/425)

Use a calculator to find arctan(40/425) ≈ 5.383 degrees.

However, it seems you are trying to find the angle clockwise from North. In navigation terms, angles are stated clockwise from North. So to get the angle you need, subtract the obtained angle (5.383 degrees) from 90 degrees:

angle = 90 - 5.383 ≈ 84.617 degrees.

Therefore, the direction of the jet is approximately 84.62 degrees clockwise from North.