To determine the temperature in degrees Fahrenheit (°F) when the temperature in degrees Celsius (°C) is given, we need to use the formula that converts Celsius to Fahrenheit. The given formula is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Here, [tex]\( C \)[/tex] is the temperature in Celsius and [tex]\( F \)[/tex] is the temperature in Fahrenheit. We need to find [tex]\( F \)[/tex] when [tex]\( C = 15 \)[/tex].
First, substitute [tex]\( C = 15 \)[/tex] into the formula:
[tex]\[ 15 = \frac{5}{9}(F - 32) \][/tex]
Next, to eliminate the fraction, multiply both sides of the equation by 9:
[tex]\[ 15 \times 9 = 5(F - 32) \][/tex]
[tex]\[ 135 = 5(F - 32) \][/tex]
Then, divide both sides by 5 to isolate [tex]\( F - 32 \)[/tex]:
[tex]\[ \frac{135}{5} = F - 32 \][/tex]
[tex]\[ 27 = F - 32 \][/tex]
Now, add 32 to both sides to solve for [tex]\( F \)[/tex]:
[tex]\[ 27 + 32 = F \][/tex]
[tex]\[ 59 = F \][/tex]
Therefore, the temperature in degrees Fahrenheit is [tex]\( 59 \)[/tex] degrees.
