MHB Finding Angle ACB in Triangle ABC

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Angle Triangle
AI Thread Summary
In triangle ABC, with angle ABC measuring 45 degrees and point D on line segment BC such that 2BD equals CD and angle DAB is 15 degrees, the goal is to find angle ACB. A point M is identified between A and D where angle MBD equals 30 degrees, leading to the conclusion that AD equals the square root of 3 plus 1. The relationship between angles results in angle CMD being 90 degrees and angle MCA being 45 degrees. Ultimately, angle ACB is determined to be 75 degrees, confirmed by multiple participants in the discussion.
Albert1
Messages
1,221
Reaction score
0
$\triangle ABC , \angle ABC=45^o,\,\, point \,\, D\,\, on \,\, \,\overline{BC} $

$and,\,\, 2\overline{BD}=\overline{CD},\,\, \angle DAB=15^o$

$find :\,\, \angle ACB=?$
 
Mathematics news on Phys.org
Albert said:
$\triangle ABC , \angle ABC=45^o,\,\, point \,\, D\,\, on \,\, \,\overline{BC} $

$and,\,\, 2\overline{BD}=\overline{CD},\,\, \angle DAB=15^o$

$find :\,\, \angle ACB=?$
Find a point $M$ between $A$ and $D$ such that $\angle MBD=30$. Note that $MD=DM$ and $AM=MB$. Say $BD=1$. The above leads to $AD=\sqrt 3 + 1$. Further note that $\angle CMD=90$ and hence $\angle MCA=45$. Consequently $\angle ACB=75$.
 
caffeinemachine said:
Find a point $M$ between $A$ and $D$ such that $\angle MBD=30$. Note that $MD=DM$ and $AM=MB$. Say $BD=1$. The above leads to $AD=\sqrt 3 + 1$. Further note that $\angle CMD=90$ and hence $\angle MCA=45$. Consequently $\angle ACB=75$.
caffeinemachine :very good solution :cool:
 
Albert said:
caffeinemachine :very good solution :cool:
Thanks. :) If you have a different one then please post it.
 

Attachments

  • Angle ACB.jpg
    Angle ACB.jpg
    16.7 KB · Views: 93
Albert said:
https://www.physicsforums.com/attachments/1209
from the diagram it is easy to see that :
$\angle ACB =30^o +45^o =75^o$
Awesome!
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
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...

Similar threads

Replies
4
Views
2K
Replies
4
Views
2K
Replies
5
Views
2K
Replies
1
Views
1K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
3
Views
2K
Back
Top