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

Option C is correct.

The length of a leg rounded to the nearest tenth is, 19.8.

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=(perpendicular)/(Hypotenuse)` then;

from the figure given below, we have,

`\sin 45^(\circ)=(DG)/(DF)`

Substitute the value of DF = 28 cm, we have

`\sin 45^(\circ)=(DG)/(28)` or

`(1)/( √(2))=(DG)/(28)` or

`(28)/( √(2))=DG`

⇒
`DG= (28)/(1.414) = 19.8019802` [ Use:
`√(2) = 1.414`]

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