Nisha is looking out the window of her apartment building at a sculpture in a park across the street. the top of nisha's window is 80 feet from the ground. the angle of depression from the top of nisha's window to the bottom of the sculpture is 20°. how far away from the building is the sculpture? round your answer to the nearest hundredth.
29.11 ft
75.18 ft
128.67 ft
219.80 ft

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

do you mean add both of the equations together

because if you do the answer is 10x-5

step-by-step explanation:

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.