Need help understanding finding this force using trig

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In summary, the conversation is about determining the maximum and minimum values of P for which a block resting on an inclined plane is in equilibrium. The solution involves using trigonometry to calculate the components of the weight and the normal force. There is a common error in using the wrong triangle to calculate the components of the weight. The full vector is always the hypotenuse of the triangle when resolving a vector into components.
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dlacombe13
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Homework Statement


The block resting on the inclined plane shown has a mass of 40kg. Determine the maximum and minimum value of P for which the block is in equilibrium. (fs=0.35 and θ=25°)

The image on top is the diagram in the book and the image below it is my free-body diagram (not too sure if the Fr (friction) force is correct though)

prob_zpsu89wywac.png


3. Attempt at the solution
Now my problem isn't exactly but how to solve this, since I found the solution online. My question is more about the trigonometry used to find some of the forces in this diagram. I found that the w (the weight) is of course (40)(9.8) = 392.4. Now the question is this:

The solution and the book claims that N=(392.4)(cos 25) = 355.64. However I am confused because if I say that:
cos 25 = a/h (N)
cos 25 = 392.4/h
h=392.4/cos 25 = 432.97
Which is incorrect. Can some explain why in my mind, I am 100% that this equation does indeed solve for the hypotenuse, yet the book claims that it is the product of the two? Is my free-body diagram wrong? I am certain i that it isn't (except maybe the friction force which may be wrong). Once I understand this I am sure I can better understand the solution to this problem and other similar problems.
 
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You are using the wrong triangle to calculate the components of the weight. (A very common error, by the way, so don't feel bad.) Note that when you resolve a vector (in this case the weight) into components using a right triangle, the full vector is always the hypotenuse of that triangle.

Read this: Inclined Planes
 
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FAQ: Need help understanding finding this force using trig

1. What is trigonometry and why is it important in understanding forces?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is important in understanding forces because forces often act at angles and trigonometry allows us to calculate the magnitude and direction of these forces.

2. How do I find the force using trigonometry?

To find the force using trigonometry, you will need to know the angle at which the force is acting, as well as the magnitude of the force. Then, you can use the trigonometric functions (sine, cosine, and tangent) to calculate the components of the force and use vector addition to find the resultant force.

3. Can you provide an example of finding a force using trigonometry?

Sure, let's say you have a force of 10 Newtons acting at an angle of 45 degrees. To find the horizontal and vertical components of this force, we can use the sine and cosine functions, respectively. The horizontal component would be 10 * cos(45) = 7.07 N and the vertical component would be 10 * sin(45) = 7.07 N. Then, we can use the Pythagorean theorem to find the magnitude of the resultant force, which would be √(7.07^2 + 7.07^2) = 10 N.

4. What other applications does trigonometry have in science?

Trigonometry is used in various fields of science, such as physics, engineering, astronomy, and surveying. It is used to calculate distances, angles, and forces in these fields, making it an essential tool for understanding and solving problems in these areas.

5. How can I improve my understanding of using trigonometry to find forces?

To improve your understanding, it is important to practice solving different types of problems involving forces and angles. You can also review the trigonometric functions and their properties to better understand how they can be used to find forces. Additionally, seeking help from a teacher or tutor can also be beneficial in improving your understanding of this concept.

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