Sine, cosine, and tangent?

Question

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?

Answer 1

Sine = cosine = 1/rt2,

tangent = 1.

Revise properties of a square. Diagonal of a square makes angle of 45 with the sides.

Answer 2

It's sin45, cos45, and tan45

sqrt2/2, sqrt2/2 and 1 respectively.

A square has 4 90 degree angles, a diagonal bisects it creating a 45, 45, 90 right triangle.

Answer 3

Well, since its a diagonal in a square tile, the angle would be 45.

sine 45 = root2 / 2

cosine 45 = root2 / 2

tan 45 = 1

Answer 4

The diagonal is the hypotenuse.

The sides are the legs.

since we cut a square, the angles are 45, 45 and 90.

the sine of an angle is the opposite side length divided by the hypotenuse length.

Cosine of an angle is the adjacent side length divided by the hypottenuse length.

Tangent is the opposide side length divided by the adjacent side length.

The triangle sine and cosine are the same.

Each leg is 12" long.  Using the Pathagorean thereom (C^2=A^2+B^2), we can calculate the hypotenuse is the the square root of 12 squared plus 12 squared.  

144 + 144 = 288

288^-2=16.970

Incedently the quick way to find the hypotenuse is the leg times the square root of 2.

Ok so sine of 45 = 12/16.970= .7071

Sine = cosine in this case.

Tangent = 12/12= 1.