NEED HELP WITH TRIG please show work as i am trying to learn the material i'm really puzzled. its soh cah toa but i don't remember how to do it

see below

Step-by-step explanation:

5.  sin 31 = opp/ hyp

  sin 31 = 34 /x

x = 34 / sin 31

x =66.0145369

tan 31 = opp /adj

tan 31    = 34/y

y = 34/ tan 31

y= 56.5855024

6.  Pythagorean theorem to find z

9^2+12^2 = z^2

81+144 = z^2

225 = z^2

z =sqrt(225) =15

sin x = opp / hyp

sin x = 9/15

take the inverse sin

x = sin^ -1 (9/15) = 36.86989765

sin y = opp / hyp

sin y = 12/15

take the inverse sin

y = sin^ -1 (12/15) = 53.13010235

1. sin(31) = opposite/hypotenuse

sin(31) = 34/x

x = 34/sin(31) = 66.0145369

x = 66.0°

tan(31) = opposite/adjacent

tan(31) = 34/y

y = 34/tan(31) = 56.5855024

y = 56.6°

2. tan(x) = opposite/adjacent

tan(x) = 9/12

x = 36.86989765

x = 36.9°

y = 180 - 90 - x

y = 53.13010235

y = 53.1°

z² = 9² + 12²

z² = 225

z = 15

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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step-by-step explanation: