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?

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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?

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Answer 1 · 2018-02-19T21:56:31

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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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

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