Question

Calculate m∠ADC. Round to the nearest thousandth.

Answer 1

Answer:  $54.508^{\circ}$

Step-by-step explanation:

Let the angle ADC = x degree

Since, By the given diagram, In triangle BDC,

$\frac{BC}{DC} = tan27^{\circ}$

⇒ $\frac{BC}{19.6} = tan27^{\circ}$

⇒ $BC = 19.6\times tan 27^{\circ}$

⇒  $BC = 9.98669881009$

Now, In triangle ADC,

$tan x =\frac{AC}{DC}$

⇒  $tan x =\frac{AB+BC}{DC}$

⇒  $tan x =\frac{17.5+9.98669881009}{19.6}$

⇒  $tan x =\frac{27.4866988101}{19.6}$

⇒  $tan x =1.40238259235$

⇒  $x = 54.508389368\text{ degree} \approx 54.508^{\circ}$