Given that sina = 2/3 and a is acute find cos(a)

Recall that

Angle is acute, which means its measure is between 0 and 90 degrees. For , we have , so we should take the positive root. Then

because 1.2 isnt half of 6 duh

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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