If sin(theta°) = 0.5, and we know that cos (theta°) < 0, then what is the smallest possible positive value of theta?

150°

Step-by-step explanation:

It is given that CosФ < 0 i.e CosФ is negative.

Therefore, the minimum the value of Ф for which CosФ <0 will be in the second quadrant i.e 90° < Ф < 180°.

Now it is also given that, Sin Ф =0.5 {the value of SinФ is positive because Sin value is positive in second quadrant.}

⇒ Ф =180° - Sin⁻¹ (0.5) = 180°-30° =150° (Answer)

what golf ball

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)