Question

Calculate m∠ADC. Round to the nearest thousandth.

Answer 1

Answer:
`54.508^(\circ)`

Explanation:

Let the angle ADC = x degree

Since, By the given diagram, In triangle BDC,

`(BC)/(DC) = tan27^(\circ)`

⇒
`(BC)/(19.6) = tan27^(\circ)`

⇒
`BC = 19.6* tan 27^(\circ)`

⇒
`BC = 9.98669881009`

Now, In triangle ADC,

`tan x =(AC)/(DC)`

⇒
`tan x =(AB+BC)/(DC)`

⇒
`tan x =(17.5+9.98669881009)/(19.6)`

⇒
`tan x =(27.4866988101)/(19.6)`

⇒
`tan x =1.40238259235`

⇒
`x = 54.508389368\text{ degree} \approx 54.508^(\circ)`