Question

The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiation control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms

Answer 1

Let the height of the cell phone tower be h m

AD is the height of the apartment; AD = 50 m

Let AB be x

In the right triangle ABC

tan 60° = `"BC"/"AB"`

`sqrt(3) = "h"/x`

x = `"h"/sqrt(3)`  ...(1)

In the right triangle ABD, tan 30° = `"AD"/"AB"`

`1/sqrt(3) = 50/x`

x = `50sqrt(3)`  ...(2)

From (1) and (2) We get

`"h"/sqrt(3) = 50sqrt(3)`

h = `50sqrt(3) xx sqrt(3)`

= 50 × 3

= 150

Height of the cell phone tower is 150 m.

Yes, the cell phone tower meets the radiation norms.