For the figure, on the pole where, tower is attached, the measure of side DC is 21.4 feet.
What is right angle triangle property?
In a right angle triangle, the ratio of the opposite side to the adjacent side is equal to the tangent angle between them.
[tex]\thn \theta=\dfrac{b}{a}[/tex]
Here, (a) is the adjacent side, (b) is the opposite side and [tex]\theta[/tex] is the angle made between them.
The height of the pole is 60 foot. Therefore,
[tex]AC=60\rm ft[/tex]
The distance of the wire from the base of the pole is 40 feet. Therefore,
[tex]BC=40\rm ft[/tex]
Therefore, the tangent angle can be given as,
[tex]\tan\angle(ABC)=\dfrac{60}{40}\\\angle(ABC)=\tan^{-1}(1.5)\\\angle(ABC)=56.31^o[/tex]
The angle DBC is half of the angle ABC. Thus,
[tex]\angle(DBC)=\dfrac{56.31}{2}\\\angle(DBC)=28.15^o[/tex]
Now, again in the triangle DBC, the tangent angle can be given as,
[tex]\tan(28.15)=\dfrac{DC}{40}\\DC=21.407\rm ft[/tex]
Hence, on the pole where, tower is attached, the measure of side DC is 21.4 feet.
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
