find the length of the antenna.

Question

A vertical antenna is mounted atop a 45 foot pole. From a point on level ground 74 feet from the base of the pole, the antenna subtends an angle of 10.6. Find the length of the antenna.

 

Answer 1

Let θ be the angle of elevation to the bottom of the antenna from the point, P, on the ground 74 feet from the base of the pole 

 

Then, tanθ = 45/74

 

              θ = Tan^-1 (45/74) = 31.3°

 

So, the angle of elevation from point P to the top of the antenna is 31.3° + 10.6° = 41.9°

 

Let x = length of the antenna

 

Then, tan41.9° = (x+45) / 74

 

         x = 74tan41.9° - 45 = 21.4 ft