how is the law of cosine used in real life?

Question

the law of sine

Answer 1

Law of sine -

A very sick man wants to get famous by plinking a high-ranking politician who will be making a speech from a podium set up on the bank of the Mississippi. Directly across the river from the podium is a large federal building that the guy would love to use, but he figures there's no way into it with a plinker. But 170 paces North of the building-centered entrance of the federal building is a nice abandoned warehouse; and 220 paces South of the same point is a small grove of trees where he can set up a transit in private. He does so, and determines that the angle between the podium and the window in the warehouse he intends to plink from is 77 degrees. Then he goes to the abandoned warehouse and measures an angle of 69 degrees between the podium and the grove of trees. What range should he adjust the elevation of his sights for?

Knowing that the sum of the angles of a triangle equals 180, he knows that the angle between the grove and the window, as viewed from the podium is 34 degrees. And since he did his job as a student and applied himself to his studies rather than whine "what use is this krap?", he knows that the ratio of the sines of angles of triangles to their opposite sides are equal, so he can quickly calculate his range as -

sin a/A = sin b/B ==

sin 34/(220+170) = sin 71/x ==

390 * sin 71/sin34 = x = 659 paces


.....

A similar solution can be had using the law of cosines. So rather than make yourself look childish, instead, do YOUR job and learn the material. You always have the option of not using it in the future, if you like. But just do it and be grateful that, for now at least, your job involves your mind and not your back. And my sincere apologies if I'm reading more into your question than you intended.

BW,
GH

Answer 2

Laws Of Cosine

Answer 3

Since the cosine and the sine describe the coordinates swept out on a circle, you tend to find these anywhere an equation deals with circles and rotation. A crane rotates, doors or anything else on hinges rotates, writing equations to describe their positions in terms of the angle of rotation will have sin and cosine terms converting those angles into locations in 2 dimensions, or even (suitably transformed) into three.

Answer 4

If you work at walmart or sears, you do not have to worry about these trigonometic laws.

However, as engineers, I use them all the time to figure out angles and length of sides of triangles.

I would think that civil/structural engineers would use them more than electrical or computer engineers.

Answer 5

there are many situations that demand the use of trig. try looking at the word problems in your text book. there are usually many examples.

Answer 6

Surveying, construction, cad/cam design tools,............ et al