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!

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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(1512) 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:
drawing%28300%2C300%2C-3%2C3%2C-3%2C3%2Cline%28-2%2C2%2C2%2C2%29%2Cline%282%2C2%2C2%2C-2%29%2Cline%282%2C-2%2C-2%2C-2%29%2Cline%28-2%2C-2%2C-2%2C2%29%2Cgreen%28line%28-2%2C2%2C2%2C-2%29%29%2Cred%28locate%28-1.8%2C-1.5%2C90%5Eo%29%29%2Cred%28locate%281.5%2C1.8%2C90%5Eo%29%29%2Cred%28locate%28-1.9%2C1.5%2C45%5Eo%29%29%2Cred%28locate%28-1.5%2C1.9%2C45%5Eo%29%29%2Cred%28locate%281.2%2C-1.5%2C45%5Eo%29%29%2Cred%28locate%281.6%2C-1.1%2C45%5Eo%29%29%2Cgreen%28locate%280%2C2.3%2C12in%29%29%2Cgreen%28locate%282.2%2C0%2C12in%29%29%2Cgreen%28locate%280%2C-2.2%2C12in%29%29%2Cgreen%28locate%28-2.7%2C0%2C12in%29%29%29

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