If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, what is the perimeter of A'B'C'D'?

A) 30 units

B) 60 units

C) 90 units

D) 120 units

219.80 ft

Step-by-step explanation:

This is a right triangle problem.  The only issue here is with the angle of depression.  The angle of depression is OUTSIDE the triangle, not inside.  However, Nisha's line of sight is parallel to the ground, and the angle of depression, geometrically speaking, is a transversal.  When a transversal cuts through 2 parallel lines, several types of angles result.  Her angle of depression is alternate interior with the base angle, and alternate interior angles are congruent.  So we know that the base angle is also 20 degrees.  The height of her window is 80 (which is the height of the triangle), and we are looking for the length of the base of the triangle.  So...we have a reference angle, a height (which is the side opposite the reference angle) and we are looking for the length of the base (which is the side adjacent to the reference angle).  These values fit into the tangent ratio formula where tangent of an angle is equal to the ratio of the side opposite the angle over the side adjacent to the angle.  Algebraically, that looks like this:

Doing some algebraic manipulating and getting x alone:

Plug this into your calculator in degree mode and you'll get that the base length is 219.80 feet