Answer:
Option C is correct.
The length of a leg rounded to the nearest tenth is, 19.8.
Step-by-step explanation:
In triangle DEF,
Given: DF =28 cm and [tex]\angle F = 45^{\circ}[/tex]
Draw a perpendicular line from the vertex D to a point G on EF.
Using trigonometric ratio:
[tex]Sine=\frac{perpendicular}{Hypotenuse}[/tex] then;
from the figure given below, we have,
[tex]\sin 45^{\circ}=\frac{DG}{DF}[/tex]
Substitute the value of DF = 28 cm, we have
[tex]\sin 45^{\circ}=\frac{DG}{28}[/tex] or
[tex]\frac{1}{ \sqrt{2}}=\frac{DG}{28}[/tex] or
[tex]\frac{28}{ \sqrt{2}}=DG[/tex]
⇒ [tex]DG= \frac{28}{1.414} = 19.8019802[/tex] [ Use:[tex]\sqrt{2} = 1.414[/tex]]
Therefore, the length of a leg (DG) rounded to the nearest tenth is, 19.8.
