Question

Anna is trying to find the height of a radio antenna on the roof of a local building. Shestands at a horizontal distance of 19 meters from the building. The angle of elevationfrom her eyes to the roof (point A) is 34°, and the angle of elevation from her eyes tothe top of the antenna (point B) is 41°. If her eyes are 1.5 meters from the ground,find the height of the antenna (the distance from point A to point B). Round youranswer to the nearest tenth of a meter if necessary.

Answer 1

Step 1: Let us draw a pictorial view of the information given:

The height of the antenna AB will be:

`AB=OB-OA`

Let us find OA from triangle OAS

`\begin{gathered} \tan 34=(OA)/(19) \\ OA=19*\tan 34 \\ OA=12.816m \end{gathered}`

Now, we will find OB from triangle OBS

`\begin{gathered} \tan 41=(OB)/(19) \\ OB=19*\tan 41 \\ OB=16.516m \end{gathered}`

Now, let us find length AB, which is the length of the antenna:

`\begin{gathered} AB=OB-OA \\ AB=16.516m-12.816m \\ AB=3.7m \end{gathered}`

The height of the antenna is 3.7 meters.