28.
TOA
Tan 120= 4000/x (multiply each side of the equation by x)
x Tan 120=4000 (divide each side by Tan 120 )
x Tan 120/ Tan 120 =4000/ Tan 120
x=4000/ Tan 120
x= 18818.52 ft
29.
TOA
Tan 100= 50/x (multiply each side of the equation by x)
x Tan 100=50 (divide each side by Tan 120 )
x Tan 100/ Tan 100 =500/ Tan 100
x=500/ Tan 100
x= 283.56 ft
30.
TOA
Tan 15.60= x/205 (multiply each side of the equation by 205)
205 Tan 15.60=x
x= 57.24 yards
31.
SOH
Sin x = 15/85
Sin x =0.1765 (Find the sin inverse of 0.1765)
x= Sin—1 0.1765
x= 10.160
32.
CAH
Cos x = 10/30
cos x =0.3333 (Find the cos inverse of 0.1765)
x= Cos—1 0.3333
x= 70.530
33.
CAH
Cos 170= 20/x (multiply each side of the equation by x)
x Cos 170=20 (divide each side by Cos 170 )
x Cos 170/ Cos 170 =20/ Cos 170
x=20/ Cos 100
x= 20.91ft
Rafter= x + overhang
Rafter= 20.91 + 1 (12 inch= 1 foot)
Rafter= 21.91 feet
34.
Sin 140= x/25 (multiply each side by 25)
25 Sin 140= x
x= 6.05 feet
35.
Cos 180= x/ 38 (multiply each side by 38)
38 Cos 180= x
x= 36.14 inches
Equations
y=x2 – 4x + 9
| X | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| X2 | 16 | 9 | 4 | 1 | 0 | 2 | 4 | 9 | 16 | 25 | 36 | 49 |
| -4x | 16 | 12 | 8 | 4 | 0 | -4 | -8 | -12 | -16 | -20 | -24 | -28 |
| 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
| y | 41 | 30 | 21 | 14 | 9 | 6 | 5 | 6 | 9 | 14 | 21 | 30 |
y=9, x=0
y=x2 + 4x + 9
| X | -7 | -6 | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| X2 | 49 | 36 | 25 | 16 | 9 | 4 | 1 | 0 | 2 | 4 | 9 |
| 4x | -28 | -24 | -20 | -16 | -12 | -8 | -4 | 0 | 4 | 8 | 12 |
| 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
| y | 30 | 21 | 14 | 9 | 6 | 5 | 6 | 9 | 14 | 21 | 30 |
y=9, x=0
y=-x2 – 4x + 9
| X | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| -x | 4 | 3 | 2 | 1 | 0 | -1 | -2 | -3 | -4 | -5 | -6 | -7 |
| -X2 | 16 | 9 | 4 | 1 | 0 | 2 | 4 | 9 | 16 | 25 | 36 | 49 |
| -4x | 16 | 12 | 8 | 4 | 0 | -4 | -8 | -12 | -16 | -20 | -24 | -28 |
| -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 |
| y | 41 | 30 | 21 | 14 | 9 | 6 | 5 | 6 | 9 | 14 | 21 | 30 |
y=9, x=0
y=x2 – 4x + 9
| X | -6 | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 |
| X2 | 36 | 25 | 16 | 9 | 4 | 1 | 0 | 2 | 4 |
| -4x | -24 | -20 | 16 | 12 | 8 | 4 | 0 | -4 | -8 |
| 9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 | -9 |
| y | 3 | -4 | -9 | -12 | -13 | -12 | -9 | -4 | 3 |
y=-9, x=0
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