Why Might Ay Be Bigger Than Ax in a Triangle?

[Make]

Homework Statement

The attached question(question 1) is in finnish, but you'll understand it no problem!;) The answers are given at the end of the text part of the question.

Homework Equations

The Attempt at a Solution

Firstly, I'm wondering how can Ay be bigger than Ax even though the X side of the little triangle at the left end of the boom is 4 and Y is 3?

Secondly, why can't I write the equation for the x dimension as follows: $$\sum$$F= -400sin15+0,8A=0

 

[Redbelly98]

A is not a normal*** force. If it were, we'd have

A_x = 3/5 A​

A must act to balance the other forces that are present. Since the other forces are close to being vertical, A is closer to vertical than to horizontal.


*** "normal" means the force is perpendicular to the surface

 

[nlightner]

?

I appreciate your curiosity and attention to detail in regards to this math question. To address your first question, it is important to remember that the sides of a triangle are relative to their angle measurements. In this case, Ay may be bigger than Ax because it is opposite the larger angle, creating a larger side length.

As for your second question, I believe you may have made a mistake in your equation. The correct equation for the x dimension would be \sumF= -400sin15-0.8A=0. This is because the force applied by the boom (0.8A) is acting in the opposite direction of the force due to gravity (-400sin15).

I hope this helps clarify any confusion and encourages you to continue exploring and questioning mathematical concepts. Keep up the good work!