Answer:
The value of DC is 66.34.
Step-by-step explanation:
The triangles ABC and DCA are right angled triangles.
The straight line AC is a bisector for angles C and A.
The measure of ∠C is 30°.
Then the measure of angles BCA and ACD will be 15° each.
The measure of angle DAB is 150°.
Then the measure of angles DAC and BAC will be 75° each.
Now consider the right angled triangle ABC.
The measure of side AC is:
[tex]AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}[/tex]
Consider the right angled triangle DCA.
The angle DAC measure 75°.
Using the trigonometric identities compute the value of Perpendicular DC as follows:
[tex]tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34[/tex]
Thus, the value of DC is 66.34.
