Question

Solve for x. Round to the nearest hundredth.

Answer 1

Answer: $32.98^{\circ}$

Step-by-step explanation:

Since, By the given diagram,

In quadrilateral ABCD, all angles are right angles ⇒ DC = AB = 15 cm and CB = DA

Also, In triangle DFA,

$sin 56^{\circ} = \frac{DA}{DF}$

⇒ $sin 56^{\circ} = \frac{DA}{16}$

⇒ $16\times sin 56^{\circ}=DA$

⇒ $13.2646011609\text{ cm} = DA$

Now, In triangle, DEC,

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

⇒ $tan x = \frac{EB-CB}{DC}$

⇒ $tan x = \frac{EB-DA}{DC}$

⇒ $tan x = \frac{23-13.2646011609}{15}$  

⇒ $tanx = \frac{9.73539883912}{15}$

⇒ $tanx = 0.64902658927$

⇒ $x = 32.9846428556^{\circ} \approx 32.98^{\circ}$