My Physics teacher presented a wrong diagram? (Explanation↓)

[mioei]

My Physics teacher told us to use a = g x sinθ during a lab trying to find how close we could calculate gravity using an inclined plane, a moving cart and a motion sensor to measure acceleration. He also drew a diagram next to the formula. I just wanted to confirm that his diagram was wrong, or whether i was looking at it incorrectly.https://gyazo.com/81845ac6ad3da72caf84e5a8d0501c83

After looking at the diagram i noticed there was no possible way a = g x sinθ could happen from that diagram. Sin = Opposite / Hypotenuse, meaning it would be g = a x sinθ. I looked up what the correct formula was and a = g x sinθ appeared. This means his diagram must be wrong or there must be something here i couldn't see. Could some one send me a correct diagram or tell me why i am wrong?

 

[nasu]

Yes, if the sides of the triangles are accelerations, the diagram is not right. The tangential acceleration (a) is less than g.

 

[Merlin3189]

I think you are mis-interpreting the diagram. The sides of the triangle do not represent the vectors and their length is not proportional to the magnitude of the vectors.
It simply shows the slope down which your cart is rolling.
The direction of the sides shows the directions of a and g, but the lengths of the sides do not show their magnitude.

If you consider various angles for theta, you can see that the formula is reasonable.
When theta is 0, g causes no horizontal acceleration.
When theta is 90deg, the slope is vertical and a = g.
In vector terms, the component of g along the slope is g cos(90 - θ) = g sin(θ)

 

[Chestermiller]

My Physics teacher told us to use a = g x sinθ during a lab trying to find how close we could calculate gravity using an inclined plane, a moving cart and a motion sensor to measure acceleration. He also drew a diagram next to the formula. I just wanted to confirm that his diagram was wrong, or whether i was looking at it incorrectly.https://gyazo.com/81845ac6ad3da72caf84e5a8d0501c83

After looking at the diagram i noticed there was no possible way a = g x sinθ could happen from that diagram. Sin = Opposite / Hypotenuse, meaning it would be g = a x sinθ. I looked up what the correct formula was and a = g x sinθ appeared. This means his diagram must be wrong or there must be something here i couldn't see. Could some one send me a correct diagram or tell me why i am wrong?

His diagram is guaranteed to confuse you, and he should have realized this. Drop a normal from the lower end of g to the hypotenuse. This will produce a new triangle. The side of this new triangle parallel to the hypotenuse will be the component of g along the hypotenuse, and will be your acceleration component.

Chet

 

[sophiecentaur]

The sides of the triangle do not represent the vectors and their length is not proportional to the magnitude of the vectors.

It happens all the time and students need to be really disciplined to choose the correct triangle for vector calculations. The teacher should have either have drawn out the vector diagram over the physical picture or warned the students that they needed to do so.
I always recommend to check you've got it right by asking yourself if the force is increasing or decreasing with the angle that's shown (by eye). In a case like this one, g is clearly the maximum available and the acceleration a would be zero if the plane were horizontal. Hence, we're talking in terms of gsine(θ). In other examples, where an angle is drawn in a different place, it can be Cos(θ) that emerges from the sums.
@mioei: it was a good idea to bring the problem to PF and you presented the question well, rather than just saying "whats the answer?" Keep in touch!