Question

CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION

Answer 1

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:

$AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}$

Consider the right angled triangle DCA.

The angle DAC measure 75°.

Using the trigonometric identities compute the value of Perpendicular DC as follows:

$tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34$

Thus, the value of DC is 66.34.