Properties of Triangle – Its engineering applications

In the textbook, we have many formulas describing properties of a triangle and a hell lot of questions. Does any wonder why we study them? What is the application of these properties? In this post, I will try to show few real life examples where such properties are used to solve them:

Let’s start with some basics on properties of triangle followed by their applications:

In triangle ABD, we have  Sinβ = AD/ c hence AD = c Sinβ  & BD = c Cosβ

Now in triangle ACD, we have a property:

             a/ Sinγ  = b / Sinβ = c / Sinα

Well, we all knew and studied it, i want to show here whats the use of this property in real life application. Lets dive it now:

Question: As shown in the diagram below, a boat is pulled by ropes by two people to the shore. How much resultant force is taking the boat out to shore:

P = 45 N, T = 55 N, θ = 30° and θ1 = 45°

So how do we solve this? Lets make this force diagram as triangular:

 In order to make a triangle we have to move the force T to the right alone the force P. You may wonder why angle  ACB = θ1? Its because line AC in triangle is parallel to force T on the left image. Now two parallel lines cut the same angle hence they are same.

Next step is to find the value of F1. Here comes the application of properties of triangle what we derived earlier.

Angle A = 180 –( θ+ θ1)  = 180-(30+45) = 105°

F1/ Sin105° = P/Sin45°

Hence, we have

F1 = 45 x √2 x  Sin105°    answer!