Question

In triangle DEF, DF=28 and angle f=45. Find the length of a leg rounded to the nearest tenth. 3.7 28.0 19.8 14.0

Answer 1

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 $\angle F = 45^{\circ}$

Draw a perpendicular line from the vertex D to a point G on EF.

Using trigonometric ratio:

$Sine=\frac{perpendicular}{Hypotenuse}$ then;

from the figure given below, we have,

$\sin 45^{\circ}=\frac{DG}{DF}$

Substitute the value of DF = 28 cm, we have

$\sin 45^{\circ}=\frac{DG}{28}$ or

$\frac{1}{ \sqrt{2}}=\frac{DG}{28}$ or

$\frac{28}{ \sqrt{2}}=DG$

⇒ $DG= \frac{28}{1.414} = 19.8019802$    [ Use:$\sqrt{2} = 1.414$]

Therefore, the length of a leg (DG) rounded to the nearest tenth is, 19.8.