From her window, Carmella looks up to the top of a neighboring building at an angle of 46°. Herangle of depression to the bottom of the building is 25°The neighboring building is 180 feet away from the building Carmella is in.How tall is the neighboring building?round your answer to the nearest tenth of a foot

Accepted Solution

Answer:[tex]270.3\ ft[/tex]Step-by-step explanation:see the attached figure to better understand the problemstep 1In the right triangle ADEFind the value of h1 See the attached figureh1=AD[tex]tan(25\°)=\frac{h_1}{180}[/tex]Solve for h1[tex]h_1=(180)tan(25\°)\\h_1=83.94\ ft[/tex]step 2In the right triangle ABCFind the value of h2See the attached figureh2=BC[tex]tan(46\°)=\frac{h_2}{180}[/tex]Solve for h2[tex]h_2=(180)tan(46\°)\\h_2=186.40\ ft[/tex]step 3Find the height of the neighboring buildingwe know thatThe height of the neighboring building is equal to[tex]h=h_1+h_2[/tex]substitute the values[tex]h=83.94+186.40=270.34\ ft[/tex]Round to the nearest tenth of a foot[tex]h=270.3\ ft[/tex]