Question

If the western component of the wind is half of the south, what is the angle of the wind with the south?

Answer 1

Based on the information about vector components and graph provided, the angle of the wind with the south is 26.57°.

What are the values of the western and southern component of the wind?

The western and southern component have a negative displacement as shown in the graph.

Let the southern component be -x

The western component is half of -x = -x/2

What is the angle of the wind with the South?

Since the angle is with the south, the trigonometric ratio to be used to find the angle is:

• Tan θ = opp/adj

Tan θ = -×/2 /-x

Tan θ = 1/2

θ = tan^-1(0.5)

θ = 26.6°

Therefore, angle of the wind with the south is 26.57°.

Learn more about about vector components at: brainly.com/question/8043832

Answer 2

Answer:

This above a triangle that models our situation.

Explanation:

We have a two componens., since we have a western componet and southern component. One travel in a southern direction. and the other travel in the west.

Let the component that travel in the south be the length of a.

According to the problem, the westard component is half of that so let that length be a/2.

Now we must find the angle of the wind in the South.

This means that what is angle that is opposite of the western componet because that angle is the most southward angle. So know we apply the tan property.

$\tan(x) = \frac{opp}{adj}$

Our side opposite of the angle we trying to find is the western component and the side adjacent to it is the southern component. Also remeber since western and Southern negative displacements, we have

$\tan(x) = \frac{ - \frac{a}{2} }{ - a}$

$\tan(x) = - \frac{a}{2} \times - \frac{1}{a} = \frac{1}{2}$

Now we take the arctan or inverse tan of 1/2.

$\tan {}^{ - 1} ( \frac{1}{2} ) = 26.57$