Calculating Weight Component on Hillside | Trig/Physics Homework Question

[maff is tuff]

Homework Statement

A boulder of weight w rests on a hillside that rises at a constant angle (alpha) above the horizontal, as shown in the figure. The boulder's weight is a force on the boulder that has a direction vertically downward.

In terms of alpha and w, what is the component of the weight of the boulder in the direction parallel to the surface of the hill?

Homework Equations

The Attempt at a Solution

I put w/sin(alpha) but this is wrong. As you can see I made the component parallel to the slope of the hill x so that means that sin(alpha)=w/x...solve for x and I get x=w/sin(alpha).

Apparently this is totally wrong.

I attached the diagram to the problem. Thanks for the help

 

[gneill]

You might want to re-evaluate the geometry of the situation. See the attached diagram.

 

[maff is tuff]

Ah okay thanks I would have never thought of that. How do we know that new angle is alpha? Is that common knowledge or a basic geometry fact? This problem was weird and hard for me because it is from chapter 1 of my book which covers models, measurements, and vectors. I read the whole chapter and it didn't discuss the concept of force at all. Thanks again.

 

[phinds]

Ah okay thanks I would have never thought of that. How do we know that new angle is alpha? Is that common knowledge or a basic geometry fact? This problem was weird and hard for me because it is from chapter 1 of my book which covers models, measurements, and vectors. I read the whole chapter and it didn't discuss the concept of force at all. Thanks again.

The fact that the "new" angle shown in gneill's diagram is alpha is so fundamentally obvious from the basics of geometry that the fact that you even have to ask leads me to think that you do not have the basic math background that is expected before you get to trig. What grade are you in? What math have you already taken?

 

[nayfie]

The fact that the "new" angle shown in gneill's diagram is alpha is so fundamentally obvious from the basics of geometry

It's obvious to me that it's the same angle just by inspection, but how would you prove it?

edit: Don't worry, just did it.

 

[maff is tuff]

It looks obvious now that it is the same angle. If you tilt everything 90 degrees then the perpendicular-to-the-slant line becomes parallel to the slant and the straight down line becomes parallel to the ground. Sorry for the dumb question; I'll try to think things over more before I post.