SOLUTION: A diagonal is drawn in a 12-in. square floor tile. Find the sine, cosine, and tangent of the angle formed by the diagonal and a side. Thank you for your help!

Algebra ->  Angles -> SOLUTION: A diagonal is drawn in a 12-in. square floor tile. Find the sine, cosine, and tangent of the angle formed by the diagonal and a side. Thank you for your help!      Log On


   

Question 193675This question is from textbook
: A diagonal is drawn in a 12-in. square floor tile. Find the sine, cosine, and tangent of the angle formed by the diagonal and a side. Thank you for your help! This question is from textbook

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Being a square having 4 equal sides and 4 equal 90%5Eo angles. It follows that the diagonal formed a 45%5Eo angle = 90%5Eo%2F2=45%5Eo

To prove this using Trigo functions, and based on a 12 inch square tile:


Solving for Diagonal: (Pyth Theorem)
D%5E2=12%5E2%2B12%5E2=144%2B144
D=sqrt%28288%29
D=16.97in
By Trigo function, (Sine-Cosine-Tangent)

Sine%28sigma%29=opp%2Fhyp=12%2F16.97
sigma=sin%5E-1%2812%2F16.97%29
red%28sigma=45%5Eo%29, correct (angle formed by the diagonal and the side)

Cosine%28sigma%29=adj%2Fhyp=12%2F16.97
sigma=cos%5E-1%2812%2F16.97%29
red%28sigma=45%5Eo%29, correct

Tangent%28sigma%29=opp%2Fadj=12%2F12
sigma=tan%5E-1%2812%2F12%29=tan%5E-1%281%29
red%28sigma=45%5Eo%29, correct


Thank you,
Jojo