SOLUTION: i triagle RST, angle S is a right angle, and cscR=17/15. What is tan T?

Algebra ->  Trigonometry-basics -> SOLUTION: i triagle RST, angle S is a right angle, and cscR=17/15. What is tan T?      Log On


   

Question 755354: i triagle RST, angle S is a right angle, and cscR=17/15. What is tan T?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

csc%28R%29=1%2Fsin%28R%29=17%2F15 --> sin%28R%29=15%2F17
In a right triangle, the sine of one acute angle is the cosine of the other, so
sin%28R%29=15%2F17=cos%28T%29
For acute angles, sine and cosine are positive and the squares of sine and cosine add up to 1.
So %28sin%28T%29%29%5E2%2B%28cos%28T%29%29%5E2=1 --> %28sin%28T%29%29%5E2=1-%28cos%28T%29%29%5E2 --> sin%28T%29=sqrt%281-%28cos%28T%29%29%5E2%29
Then,
For any angle, tan%28T%29=sin%28T%29%2Fcos%28T%29,
so tan%28T%29=%28%288%2F17%29%29%2F%28%2815%2F17%29%29 --> tan%28T%29=%288%2F17%29%2A%2817%2F15%29 --> highlight%28tan%28T%29=%288%2F15%29%29