How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

1 Answer
Feb 19, 2018

Use the identities.

Explanation:

The answers you come up with are going to depend on whether you're evaluating A or B. For the sake of this answer, we can look at A.

We are given the lengths of all sides. c is the side across from C, a across from A, and b across from B.

Drawing a model at this point is helpful.

Image courtesy of me and Microsoft Paint.

We know the identities of the three normal trig functions:

SOH
sinθ=oppositehypotenuse

CAH
cosθ=adjacenthypotenuse

TOA
tanθ=oppositeadjacent

We can just substitute in our values:

  • sinA=2029
  • cosA=2129
  • tanA=2021

And flip them for the inverse functions.

  • cscA=2920
  • secA=2921
  • cotA=2120

We could easily do the same for B, flipping our values for opposite and adjacent.

  • sinB=2129
  • cosB=2029
  • tanB=2120
  • cscB=2921
  • secB=2920
  • cotB=2021