Question

CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION

Answer 1

The value of DC is 66.34.

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√(3))^(2)}\\=√(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)=(DC)/(√(316))\\\\DC=3.732*√(316)\\\\DC=66.34`

Thus, the value of DC is 66.34.