To convert the temperature from Celsius to Fahrenheit, we start with the given formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
We are given [tex]\( C = 15 \)[/tex] degrees Celsius and need to find the corresponding Fahrenheit temperature [tex]\( F \)[/tex].
1. Rearrange the formula to solve for [tex]\( F \)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Multiply both sides by 9 to eliminate the fraction:
[tex]\[ 9C = 5(F - 32) \][/tex]
2. Isolate [tex]\( F \)[/tex]:
First, divide both sides by 5:
[tex]\[ \frac{9C}{5} = F - 32 \][/tex]
Then, add 32 to both sides to solve for [tex]\( F \)[/tex]:
[tex]\[ F = \frac{9C}{5} + 32 \][/tex]
3. Substitute the given value of [tex]\( C \)[/tex] (15 degrees Celsius):
[tex]\[ F = \frac{9 \times 15}{5} + 32 \][/tex]
4. Calculate the value:
[tex]\[ F = \frac{135}{5} + 32 \][/tex]
[tex]\[ F = 27 + 32 \][/tex]
[tex]\[ F = 59 \][/tex]
Therefore, the temperature in degrees Fahrenheit is [tex]\( 59 \)[/tex] degrees.
