MHB Show Cos A = 1/12 in Square ABCD

  • Thread starter Thread starter Bushy
  • Start date Start date
  • Tags Tags
    Triangle
Click For Summary
To demonstrate that cos a = 1/12 in square ABCD, the law of cosines is suggested as a key tool. The approach involves applying the law of cosines twice: first to triangle AEC to determine side EC, and then to triangle CED to calculate cos a. This method leverages the relationships between supplementary angles to facilitate the calculations. The discussion indicates that this two-step application is essential for reaching the desired result. Ultimately, the law of cosines provides a structured way to solve for cos a in this geometric context.
Bushy
Messages
40
Reaction score
0
View attachment 467In square ABCD need to show $cos a = \frac{1}{12}$
 

Attachments

  • untitled.JPG
    untitled.JPG
    5.6 KB · Views: 97
  • untitled.JPG
    untitled.JPG
    6.6 KB · Views: 92
Mathematics news on Phys.org
While I haven't worked this problem yet, I am thinking the law of cosines may help, along with the relationship between supplementary angles.
 
I gave it some thought, and I believe applying law of cosines twice will do the trick. First you apply to the triangle $AEC$ to find side $EC$, and then apply it to the triangle $CED$ to find $\cos a$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB What is the area of square ABCD with OQ = OF = 6?
  • · Replies 3 ·
Replies
3
Views
1K
MHB What is the Surface Area of a Square with Given Points and Side Lengths?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Proof of Parallelogram ABCD: Midpoint X & Y Show Area $\frac{1}{4}$
  • · Replies 5 ·
Replies
5
Views
2K
MHB Find A in abcd=A(four digital number) is a perfect square ,given ab=2cd+1
  • · Replies 2 ·
Replies
2
Views
2K
MHB ASVAB circle and inscribed rectangle area problem
  • · Replies 6 ·
Replies
6
Views
2K
MHB Proving $abcd\ge 3$ with $a, b, c, d>0$
  • · Replies 1 ·
Replies
1
Views
1K
MHB Length of $\overline{CE}$ in Square $ABCD$ with $45^o$ Angle
  • · Replies 1 ·
Replies
1
Views
2K
Justifying Equilateral Triangle AEF in ABCD
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
36K
MHB Finding the Area of Triangle ABQ in Rectangle ABCD with Given Points and Lengths
  • · Replies 1 ·
Replies
1
Views
1K