If angle theta is an acute angle such that cos theta =1/4, find sin theta/2

The answer is ⇒ sinФ/2 = 0.612

Step-by-step explanation:

∵ cosФ = 1/4

∴ Ф = cos^-1 1/4 = 83.91°

∴ Ф/2 = 83.91 ÷ 2 = 41.96°

∴ sinФ/2 = 0.612

Step-by-step explanation:

Recall and apply the following formula;

Since is acute,

Given , then

a - base

b - exponent

so,

< 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)