# cosines

1. ### 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. ### 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...

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4. ### 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. ### 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. ### 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. ### 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...

9. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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?