if 0 < b ≤ 90 and cos(11b + 2) = sin(12b − 4), what is the value of b?
b = 3
b = 4
b = 5
b = 6

4

Step-by-step explanation:

You can plug in the b's and see.  You can also try to use a co-function identity and get a value for b that way.

Let's try the co-function identity:

sin(x)=cos(90-x).

First step:

cos(11b+2)=cos(90-[12b-4])

 So one set of solutions can be found by solving:

11b+2=90-[12b-4]

Distribute:

11b+2=90-12b+4

Add 12b on both sides

23b+2=90+4

Simplify:

23b+2=94

Subtract 2 on both sides:

23b     =94-2

23b      =92

Divide both sides by 23:

  b=       92/23

  b=        4

So 4 is one value that will work.

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+

25.45584

step-by-step explanation: