Which relationship in the triangle must be true?
sin(b) = sin(a)
sin(b) = cos(90 - b)
cos(b) = sin(180 - b)
cos(b) = cos(a)
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sube

sin(B)=cos(90-B)

Step-by-step explanation:

sin(B)=cos(90-B) is a co-function identity.

We can also prove it using the difference identity for cosine.

Let's do that:

cos(90-B)

equals

cos(90)cos(B)+sin(90)sin(B)

0cos(B)+1sin(B)

0+sin(B)

sin(B)

Therefore cos(90-B)=sin(B).

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional