Question

Please explain and give an example:

Planar Trigonometry, Right trianges, laws of sine and cosine.

Please type answer do not hand write. Thank you

Answer 1

Planar Trigonometry - It is mostly related to a right-angles triangle where one of the angle is 90 degree. This has so many standard relations. Let's take one example

Using planar trigonometry, we can write

sin (theta) = B/A

cos (theta) = C/A

tan (theta) = B/C

also, sin (theta) / cos (theta) = tan (theta)

sin² (theta) + cos² (theta) = 1

Right Triangle - The above diagram is a right triangle. It is that triangle in which one angle is 90 degree. Other two angles can be anything as long as their sum is 90, so that total sum of angles is 180

Law of sines = This law states that the ratio of a side of a plane triangle to the sine of the opposite angle is the same for all three sides.

Referring to the above diagram, by sine rule, we have

A / sin Z = B / sin X = C / sin Y

Law of cosines = The Cosine Rule states that the square of the length of any side of a triangle equals the sum of the squares of the length of the other sides minus twice their product multiplied by the cosine of their included angle. ?

Referring to the above diagram , by cosine rule we have

A² = B² + C² - 2*B*C*cos(Z)