Solving word problem given angles of elevation and finding heivht

Question

The First State Bank and a hospital are 40 meters apart. From a window in the bank, the angle of elevation to the top of the hospital is 77 degrees. From the same window the angle of depression to the ground at the base of the hospital is 61 degrees. Find the height of the hospital rounded to the nearest tenth

Answer 1

Hannah,

This is a fairly straight forward trig problem as long as you get the diagram right.  I will attempt a crude one for reference.

                                                  __________

                                                /|                 |                                                       

                                           /     |   Hosp.      |                                        

________                        /          |                 |                                                                                                   

|            |                /             h₂ |                |                                                                                                   

|            |       /      77º                |                 |                                                                                              

| Bank    |/ __________________ |                 |                                                                                           

|            |\            61º                 |                 |                                                          

|            |            \                 h₁ |                 |                                                                                          

|            |                      \            |                 |                                                                                           

|            |            40m               \ |                 |                                                                                            

__________________________________________________

 

Hopefully, you can see now that there are two right triangles in which we know an additional angle and a leg. The other leg is the height of the hospital above and below the point of view.

 

h₁ = 40*tan(61) = 72.16

 

h₂ = 40*tan(77) = 173.26

                         ______________

Total height        = 245.42  OR   245.4 m

 

I hope that helps.