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
lechugamaestro19
Feb 19, 2018

Use the identities.

Explanation:

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

We are given the lengths of all sides. #c# is the side across from #angleC#, #a# across from #angleA#, and #b# across from #angleB#.

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
#sintheta = (opposite)/(hypoten\use)#

CAH
#costheta = (adjacent)/(hypoten\use)#

TOA
#tantheta = (opposite)/(adjacent)#

We can just substitute in our values:

  • #sinA = 20/29#
  • #cosA = 21/29#
  • #tanA = 20/21#

And flip them for the inverse functions.

  • #cscA = 29/20#
  • #secA = 29/21#
  • #cotA = 21/20#

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

  • #sinB = 21/29#
  • #cosB = 20/29#
  • #tanB = 21/20#
  • #cscB = 29/21#
  • #secB = 29/20#
  • #cotB = 20/21#
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