Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin60° = 
, cos60° = 
sin45° = cos45° = 
Using the sine ratio on the right triangle on the left
sin60° = 
= 
=
Cross- multiply
2a = 4
× = 12 ( divide both sides by 2 )
a = 6
Using the cosine ratio on the same right triangle
cos60° = 
= 
=
Cross- multiply
2c = 4 ( divide both sides by 2 )
c = 2
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Using the sine/cosine ratios on the right triangle on the right
sin45° = 
= 
=
Cross- multiply
b = 6
cos45° = 
= 
=
Cross- multiply
d = 6 ( divide both sides by )
d = 6
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a = 6, b = 6, c = 2, d = 6
Let's put these as improper fractions.
30 = 60/2. add the 1/2 to get 61/2
13 = 52/4. add the 3/4 to get 55/4
To add/subtract fractions, they must have the same denominator. (bottom no.)
If we multiply the top and bottom of a fraction by something, it stays equal.
We can conclude that 61/2 = 122/4. (bottom multilpies by 2, so does the top)
Now that we have a common denominator, we can subtract.
The "fourths" just sort of acts like a unit. Subtract 55 from 122 to get
.
We can convert this to an improper fraction simply by dividing 67 by 4.
This leaves us with 16, and a remainder of 3. Our answer is
She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.
Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,
let c represent carpenter hours and b for blacksmith hours.
20c + 25b = 690
c + b = 30
Subtract b from each side so that c = 30 - b
Plug this value into the first equation
20(30 - b) + 25b = 690
600 - 20b + 25b = 690
600 + 5b = 690
5b = 90
b = 18
To find c, plug this value of b into the other equation
c + 18 = 30
c = 12
I believe is 4.9. I hope that helps
