ok proving that thest two angles are equal
Gesh almost done lol :O
h t t p : / /w w w .a n g e l f i r e. c o m / s ta r s / d h s ph y s i c s / f r ic t i o n . j p g
ok
How to prove this? Similar triangles.
Notice the upper angle in that photo is a right angle (ramp to Fn),
yes and i agree right anlge
in which the angle of Fn to the vertical is an angle complement to Fp and the vertical.
ok so your saying that...
angle Fn Fw
is complement to angle
fp and fw
because triangle adds up to 180 degrees ok understand but I need to find a proof for right triangles that the sum of their angles add up to 180 if you could show me one that would be great...!!!
Well, the ramp angle is also a complement to that angle.
huh so angle of the ramp is complemtary to angle Fw Fp...
ok i can visually see that but how do we now these two angles are complementary?????????
Therefore, ramp angle = angle Fn to vertical.
I agree... now snese both angles are completary to this other angle then they must be equal
ok just need a proof of why the angles in right triangle add up to 180 i looked on the internet couldn't find one and why those two angles are complementary...
and that's it =]
two angles are complementary if they add to a right triangle (ninety degrees). Fn is normal(right angle) to the ramp.
To prove that the two angles are equal, we need to show that they are complementary angles.
First, let's establish why the angles in a right triangle add up to 180 degrees.
In a right triangle, one angle is always 90 degrees (the right angle). Let's call this angle A.
The other two angles can be labeled as B and C.
Now, draw a straight line that extends one side of the right triangle so that it forms a right angle with that side. This creates a new triangle.
In this new triangle, we have angle A, which is 90 degrees, and two angles B and C.
Since the sum of angles in any triangle is always 180 degrees, we can say that:
Angle A + Angle B + Angle C = 180 degrees.
Substituting the value of angle A as 90 degrees, we have:
90 degrees + Angle B + Angle C = 180 degrees.
Simplifying the equation, we get:
Angle B + Angle C = 90 degrees.
This proves that the angles in a right triangle add up to 90 degrees.
Now, back to our original problem.
We know that the upper angle in the given photo is a right angle. Let's call this angle R.
The angle from Fn to the vertical line can be labeled as angle P.
The angle from Fn to the ramp can be labeled as angle F.
Since angle R is a right angle, it measures 90 degrees.
Now, if we look closely, we can see that angle P and angle F are complements of each other.
How do we know this?
Recall that we established earlier that the angle from Fn to the vertical line is complementary to angle P and angle F. Since angle R is a right angle, it is complementary to both angle P and angle F.
Therefore, angle P and angle F are complementary angles.
And because complementary angles are equal to 90 degrees, we can conclude that angle P is equal to angle F.
Hence, the two angles in question (angle Fn Fw and angle Fp Fw) are equal to each other.