Emery looks out their apartment window to the building across the way. The building isknown to be 42 feet tall. The angle of depression from Emery's window to the bottom of the buildingis 27◦, and the angle of elevation to the top of the building is 23◦. Find Emery's distance x from thebuilding across the way.

Step-by-step explanation:

From the question we are told that:

Height

Angle of depression

Angle of Elevation

Generally the equation for the vertical distance between Emery's distance x and the bottom of the building  is mathematically given by

Since the angle of depression and elevation are given as

27 and 23 respectively

Therefore

Emery's view of the 42 ft building is

Therefore Emery's distance x to the base of the building h' is

Generally the Trigonometric equation for Emery's distance x is mathematically given by

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)