MHB Derive a Generalised Formula for c-d with Respect to θ

  • Thread starter Thread starter mfaisal
  • Start date Start date
  • Tags Tags
    Triangle
AI Thread Summary
In the discussion, the relationship between the sides of a right triangle is explored, specifically focusing on the projection of side b, denoted as d, in relation to the angle θ. It is established that when θ equals 0, side b equals side c, and when θ equals 90, side d equals 0. The goal is to derive a generalized formula for the difference c - d as a function of θ. The conversation emphasizes using trigonometric functions to express the ratio of d to b. A clear formula will help in understanding the geometric relationships in the triangle.
mfaisal
Messages
1
Reaction score
0
View attachment 5681

In the above given triangle when θ = 0 then b=c
But when θ = 90 then d=0
Since d is the projection of b
How we can derive a generalised formula for d or c-d with respect to θ
Plese may kindly be elaborated
 

Attachments

  • triangle question image.png
    triangle question image.png
    2.1 KB · Views: 82
Mathematics news on Phys.org
Hello and welcome to MHB! (Wave)

Look at the right triangle, having side lengths $b,\,d,\,h$. Using a trigonometric function, what is the ratio of $d$ over $b$?
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

B Calculating the perfect tennis shot using vectors
Replies
2
Views
2K
A Can the Unwrapped Phase Function of a Fourier Transform be Derived?
Replies
1
Views
1K
MHB Solving a Primary Math Problem: Find the Areas of A & C
Replies
10
Views
2K
I Possible simple formula for ellipse circumference
Replies
6
Views
2K
MHB Find ∠A & ∠C in Triangle Geometry
Replies
1
Views
2K
MHB [ASK]Solution Set of a Trigonometry Inequation
Replies
4
Views
1K
I Generating Divergence Equation In Cylindrical Coordinates
Replies
3
Views
2K
MHB Internal angle sum of triangle
Replies
1
Views
2K
Derivation of uncertainty formula
Replies
7
Views
2K
MHB Can We Construct a Triangle with Given Lengths and Find Its Area?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top