# cosines

1. ### Cosines law, 2x

Looking for solutions of these two
2. ### Law of Cosines problem

I'm trying to find angle B using the law of cosines. I'm not sure where my mistake lies. I'm guessing somewhere in my order of operations, but I'm not 100% sure. The given sides and angle are as follows: (b=78ft; c=85ft; A=72°). I found side "a" to be 95.97 ft (the textbook answer key rounds to...
3. ### Which of the following problem types can always be solved using the law of cosines...

Which of the following problem types can always be solved using the law of cosines or sines? Check all that apply. Please explain answers. Thank you!
4. ### In order to apply the law of cosines to find the measure of an interior angle...

In order to apply the law of cosines to find the measure of an interior angle, it is enough to know which of the following? A. The area of the triangle B. The length of all three sides of a triangle C. At least two of the angles of a triangle and the length of one of its sides Please...
5. ### Law of Cosines Word Problem

Can anyone help me to answer this one..Two ships leave the same port at the same time, One ships sails on a course of 125 degree at 18 knots while the other sails on a course of 230 degree at 24 knots.Find after 3 hours (a) the distance between a ship and (b) the bearing from the first ship to...
6. ### Find the Missing parst of the Triangle Using the Laws of Cosines

Hey people. Here's the question. Find the missing parts of the triangle by using the laws of cosines. What's known is, B=27, a=11, c=22 Solving for b, b^2=11^2+22^2-2(11)(22)(cosB) b^2=121+484-2(242)(.891) b^2=605-432 b^2=\sqrt{173} b=13.2 Solving for A...
7. ### The triangle inequality, the law of cosines, cauchy inequality and variance of (X-Y)

The triangle inequality, the law of cosines, cauchy inequality and variance of (X-Y). The law of cosines c^2 = a^2 +b^2 - 2abCos(theta) looks a lot like the variance of (X-Y) where X and Y are random variables and cosine is replaced by covariance...but why? What is the relationship between...
8. ### Applying the Laws of Sines or Cosines

Solve the triangle. A = 19°, C = 102°, c = 6 choices are B = 31°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 2, b ≈ 5.3 B = 59°, a ≈ 18, b ≈ 15.8 B = 59°, a ≈ 18, b ≈ 5.3
9. ### Applying the Laws of Sines or Cosines

Solve the triangle. B = 36°, a = 41, c = 17 choices are b ≈ 29, C ≈ 20, A ≈ 124 b ≈ 44, C ≈ 20, A ≈ 124 b ≈ 29, C ≈ 121, A ≈ 23 b ≈ 44, C ≈ 24, A ≈ 120
10. ### Cosine identity

I came across the following while doing integration: I don't need a proof, I just want to understand what general property (law, theorem, identity?) of trig that is at work here. Thanks, Giest
11. ### Law of Cosines - SAS

So, I am given SAS. Now I must find the remaining angles and side. I am given: M<A= M<B=20 degrees M<C= a=10mm b= c=15mm and the triangle looks somewhat like this: ......10mm B\---------|C ...\20........| ....\...........| .....\..........| ......\.........| .......\........|...
12. ### Law of Cosines - Solve This Triangle

[SOLVED]Law of Cosines - Solve This Triangle Law of cosines problem: "Use the Law of Cosines to solve the triangle." ...............C ............./..| .........../....| 5.4 yd /......|4.2 yd ......../.......| ......./.......| .....A------B ......2.1 yd So, M<A= M<B= M<C= a=4.2 yd b=5.4 yd...
13. ### direction ratios and direct cosines

please give the short form method to solve the following. If the direction ratios of the lines are given by 3lm-4ln+mn=0, l+2m+3n=0. Then find the angle between the lines. regards Lokanadhareddy
14. ### Solving Vector Triangles (Law of Sines and Cosines possibly)

Hey all, I really don't know where to begin this problem. Three vectors, Vector AO is 400 in magnitude and direction going in -x from point A to O. (or can rearrange I believe to make another triangle piece) Vector AB is unknown going from point A to B. Vector AC is 525 in magnitude going from...
15. ### complex algebra? series sum of sines or cosines

how do i calculate the sum of each of these series? sin(A) + sin(A+B) + sin(A+2B) + sin(A+3B) .... + sin(A+(n-1)B) cos(A) + cos(A+B) + cos(A+2B) + cos(A+3B) .... + cos(A+(n-1)B) please show step by step how to do it, not just the answer.
16. ### The product of sines and the product of cosines of (k\pi)/(2n+1) for 0<k<n+1

I have to prove the following identities: \prod_{k=1}^n \cos\frac{k\pi}{2n+1}=\frac{1}{2^n} \prod_{k=1}^n \cos\frac{k\pi}{2n+1}=\frac{\sqrt{2n+1}}{2^n} The suggestion is to prove and use this: \sum_{k=0}^{2n}z^k=\prod_{k=1}^n \left (1-2z\cos\frac{2k\pi}{2n+1}+z^2\right ) for z\in\mathbb{C}...
17. ### Relation between cosines and lenghts of triangle

Prove that in any triangle we have the following relation \frac{a+b+c}{R}=8\cos{\frac{A}{2}}\cos{\frac{B}{2}}\cos{\frac{C}{2}}
18. ### Using Law of Cosines

Here is the problem (It's actually an example in a review book... Their explanation is insufficient for me.) Find the number of degrees in the largest angle of a triangle whose sides are 3, 5, and 7. They then use the law of cosines and come up with cosC=-1/2. Since cosC<0 and <C is an...
19. ### Law of Cosines problem

Hi, I am asked to solve the triangle ABC with the given information: A=115 deg. b=46.8 c=51.3 First I solved for side "a" and discovered it be to "82.8." Subsequent to this, I tried to find out what angle "B" was. Setting up the law of cosines equation (b^2=a^2+c^2-2acCosine B) and plugged in...