Two guy wires from the top of a 240foot radio antenna are an

Two guy wires from the top of a 240-foot radio antenna are anchored to the ground by two large concrete posts. The antenna is perpendicular to the ground and between the two posts. If the angles of depression from the top of the antenna to each of the posts is 32 degrees and 46 degrees then the distance between the two posts is________feet.

Solution

Here in both right triangles, we use the formula that

tan x= height/base

So in left right triangle,

tan 32 = a/240   (where a is the left base)

or 0.6248 = a/240

or a= 0.6248(240 ) =149.9

and in right side triaingle,

tan 46= b/240

or 1.0355 = b/240

or b= 1.0355(240) = 248.53

so total distance between two poles = a+ b = 149.9 + 248.53

= 398.42 feet

thatis last required answer.