How tall is the other building?

Question

A surveillance camera is mounted on top of a building that is 80m tall. The angle of elevation from the camera to the top of another building is 42 degress. The angle of depression from the camera to the base of the same building is 32 degress. 

Answer 1

I think a diagram really helps here:

 

Other Building Top

                        |    \

                        |            \

                     Y |                    \

                        |          42 degrees   

........................|.............X............. Surveillance Building Top

                        |          32 degrees |

             80 m  |               /              | 80 m

                        |     /                        |

______________|__________________|_____ground_

 

Find Height of the Other Building = 80 + Y.  Note that X represents the unknown distance between the two buildings.  We won't need to find the X itself but will need it to get the value for Y.

 

From the top triangle: Y/X = tan(42)  so Y = X tan(42).

 

From the bottom triangle: 80/X = tan(32)  so X = 80/tan(32).

 

Putting this together you should be able to substitute these expressions to find that the other building's height is equal to 80 + tan(42)[80/tan(32)], which you can simplify using your calculator, rather than writing out approximations for the tangent values, just make sure you're calculator is set to "degree" mode, not "radians".  Hope that helps!