2. A surveyor is 140 feet from a tower; the tower is 96 feet high. The surveyor's
instrument is 14.75 feet above the ground. If the surveyor sights the top of
the tower with his instruments, what is the angle of elevation?
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Answer:
Step-by-step explanation:
For these given information,let us construct a diagram.The distance between the tower and the surveyor remains constant,while the height of the tower will change because of the instrument.(See diagram below)
Apparently,the line of sight has risen by 14.75 ft,so we need to subtract the height of the tower from 14.75 feet.We get 81.25 feet,which is now the nwe height of the tower.
We will use Tangent function here,as the net height of the tower serves as the opposite side of theta and the distance between surveryor and tower as adjacent side.We now just substitute values:
Tan(Theta)=81.25/140
Theta=Tan^-1(81.25/140)
Theta(Angle of Elevation)≈30.13°
Checking:
Tan(30.13)=81.25/140
0.58=0.58
This proves that our answer is correct.