cosines

  1. J

    triangle length with cosines

    Hi guys just need some help. being given this and havent got a clue. if you could work it out and then explain that would be great Points P+Q are on opposite sides of a straight tunnel. A third point R forms a triangle PQR. S+T are established along the sides PR and QR repectively such...
  2. B

    Function using law of sines and cosines

    Create a function for this scenario. Theres a car traveling at angle theta. It is traveling at say 20.55 mph. It has to travel a total of 13.5 miles. This is in quadrant 3 of a unit circle heading away from the center. I need to find a function to represent the possible different angles the...
  3. G

    Law of Cosines Derivation

    None
  4. J

    derive the law of cosines

    how is it again that you would derve the law of cosines? i do know that it starts out like the distance formula. help plz (Talking)
  5. K

    Law of cosines

    okay i dont know why, this may be extremely easy but i'm just not getting the right answer :( Here's the question: richmond is 200 kilometers due east of Teratown and Hamilton is 150 kilometers directly north of Teratown. Find the shortest distance in kilometers between Hamilton and...
  6. Melancholy

    Law of Cosines (finding side x in a triangle)

    Find x to the nearest tenth. Okay, so according to the Law of Cosines: a^2 = b^2 + c^2 - 2bc (cos A) b^2 = a^2 + c^2 - 2ac (cos B) c^2 = a^2 + b^2 - 2ab (cos C) This is what I have so far: a^2 = 32^2 + 23^2 - 2(32)(23) (cos A) a^2 = 1024 + 529 - 1472 (cos A) a^2 = 1553 - 1472 (cos...
  7. P

    LAw of sines and Law of Cosines

    Could someone solve for x using 2 different methods- Law of Sines and Law of cOSINES. And also, can someone explain to me the difference between the two, and how you know which one to use- law of sines or law of cosines or both. If someone could solve this step by step, I'd appreciate it. I...
  8. B

    Train word problem (possibly involving law of cosines?)

    Answered, thanks!
  9. S

    Law of Cosines

    If \bold{C} = \bold{A} + \bold{B} Then \bold{C} \cdot \bold{C} = (\bold{A} + \bold{B}) \cdot (\bold{A} + \bold{B}) |\bold{C}|^{2} = |\bold{A}^{2}| + |\bold{B}^{2}| + 2|\bold{A}||\bold{B}| \cos \theta where \theta is the angle between the extension of \bold{A} and \bold{B} . Then...
  10. O

    Law of cosines 2 solutions

    In a triangle, I know angle a and opposing side A. I also know side B. Now I use law of cosines to calculate the remaining side C. But there are two solutions. How do I find both of them? I mean, I find one of them, but how do I derive the other solution? I have solved it in a clumsy...
  11. Tomato

    Derivation of Law of Cosines (excerpt)

    Prove that a=b \cos{C}+c \cos{B} I have that \cos{C}=\frac{x}{b} \implies x=b \cos{C} \cos{B}=\frac{a+x}{c} \implies x=c \cos{B}-a Hence, a=c \cos{B}-b\cos{C} A difference instead of a sum??
  12. D

    principle root and cosines.

    Hi MHF, I needed help on two question please, that are: 1] Find the three cube roots of 8(cos 264º + j sin 264º) and state which of them is the principal cube root. Show all three roots on an Argand diagram. 2] i) Expand sin 4θ in powers of sinθ and cosθ. ii) Expand cos^4θ in...
  13. K

    Law of Cosines

    Could someone please help me with this problem. Thanks Two ships leave harbor at the same time. The first sails N 15 degrees W at 25 knots (a knot is one nautical mile per hour). The second sails N 32 degrees E at 20 knots. After 2 hr, how far apart are the ships?
  14. K

    The Law of Cosines

    I am having problems with this problem. Any help would be greatly appreciated. Two airplanes leave an airport at the same time. The first flies 150 km/h in a direction of 320 degrees. The second flies 200 km/h in a direction of 200 degrees. After 3 hr, how far apart are the planes?