sine rule and cosine rule?

Question

A friend of yours approaches you and says, “I heard you are learning about sine
rule and cosine rule, why do they keep talking about those things? They’re useless
and I never understood them.” In less than (or equal to) 5 pages, explain to your
friend what is sine rule and cosine rule and talk about why such a thing is useful
in the real world.

Answer 1

cosine rule: a^2 + b^2 = c^2 + 2ab cos θ

sine rule: sin A / a = sin B / b = sin C / c

These two rules are used to find the unknown sides or angles of a triangle, given the rest of angles or sides. These triangles can exist in the real world e.g, a building.

Answer 2

The 'Law of Sines' and the 'Law of Cosines' are the most general purpose rules known relating the sides and angles of triangles. (About this point someone always says, "What about Pythagorean Theorem?" and I mention that it's a special case of the Law of Cosines.)

Why are furmulas concerning lengths and angles of triangles all that important? Without them, we couldn't survey large areas of land. We couldn't navigate across the Ocean or through space. We couldn't do about 90% of the Science and Engineering that we do (since huge quantities of modern science are based on problems and theorems that involve triangles).

In short; Without them, civilization as we know it simply would not exist.

HTH ☺

Doug

Answer 3

sines and cosines are just as important as the Pythagorean theorem.

See with the pythagorena theorem one has to have the length of two sides to find the last. (the distance to an objects bottom and top to find the height, etc)
However, with sine and cosine all we need is one length and an angle, and we can get all the other sides and angles from that.
In real life this helps with the height of buildings, and the distance one thing is from two other things.

Answer 4

if a triangle ABC , then the cosine rule for the triangle is:
A' ^2=B' ^2+C' ^2-2B'C' * cos(A) where A',B',C' are the lines opposite to the angles A,B,C consequentlr
Sine rule====>>>> sin(A)/A' = sin(B)/B' = sin(C)/C'

both the rules are important in triangle solving and VECTORS, esp in physics,,,, for knowing the direction of multiple forces.

For me i'm an archetict, and they both help me alot in designing


good luck

Answer 5

the only thing I remember is soh cah toa

and that if you learn these you can find any angle/side measurement on a triangle.

good luck and do some reading to understand the above and put that understanding in to you OWN words.. to write the essay.

Answer 6

to know height, length, size without actually measuring it.. basic rule helped in scientific progress.. in helping you get a mobile.. by studying waves.. listen music..