Question

Find DC.



DC =

(50 points)

Answer 1

I can’t see the picture

Answer 2

30.4 units

Explanation:

Step 1:

Calculate BD:

In ∠ABD

Hypotenuse = AB

= 20 units

With respect to Ф = 54°

Opposite = BD

BD can be calculated using trigonoteric function sinФ

sinФ =
`(Opposite)/(Hypotenuse)`

∴sin54° =
`(BD)/(20)`

Cross-multiplication is applied:

`(1)(BD) = (20)(sin54^(o))`

`BD = 20sin54^(o)` units

Step 2:

Calculate DC:

In ∠BDC

With respect to Ф = 28°

Opposite = BD

=
`20sin54^(o)` units

Adjacent = DC

DC can be calculated using trigonoteric function tanФ

tanФ =
`(Opposite)/(Adjacent)`

∴tan28° =
`(20sin54^(o))/(DC)`

Cross-multiplication is applied:

`(DC)(tan28^(o)) = 20sin54^(o)`

∴DC =
`(20sin54^(o))/(tan28^(o))`

= 30.4 units (Rounded off to 3 significant figures)