Answer:
1.98
Step-by-step explanation:
The triangle in the figure is a right triangle, which has a 90 degrees angle.
The side opposite to the right angle is called hypothenuse, and it is the longest side of the triangle.
For a right triangle, the following relationship exists between angles and sides:
[tex]sin \theta = \frac{opposite}{hypothenuse}[/tex] (1)
[tex]cos \theta=\frac{adjacent}{hypotenuse}[/tex]
where [tex]\theta[/tex] is any of the other 2 angles in the triangle, and opposite means "side opposite to the angle" and adjacent means "side adjacent to the angle".
In this problem, we know that the angle at D is
[tex]\theta=26^{\circ}[/tex]
We also know that the hypothenuse is
[tex]hypothenuse=DF=4.5[/tex]
Therefore, in order to measure EF, we can use eq.(1). We find:
[tex]sin \theta = \frac{EF}{DF}\\EF=DF sin \theta = (4.5)(sin 26^{\circ})=1.98[/tex]
