Given:
The triangle DEF is a right triangle.
The length of EF is 12 units.
The length of DE is y units.
The measure of angle D is 25°
We need to determine the value of y.
Value of the variable:
The value of the variable y can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{EF}{DE}[/tex]
Substituting [tex]\theta=25^{\circ}[/tex], EF = 12 and DE = y, we get;
[tex]tan \ 30^{\circ}=\frac{12}{y}[/tex]
Simplifying, we get;
[tex]y=\frac{12}{tan \ 30^{\circ}}[/tex]
[tex]y=\frac{12}{0.577}[/tex]
[tex]y=20.797[/tex]
Rounding off to the nearest tenth, we get;
[tex]y=20.8[/tex]
Thus, the length of the variable y is 20.8 units.
