Question

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?

Answer 1

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.

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`