the figure below shows a 60 foot pole held in place by wires anchored at point B, 40 feet from the base of the pole.

For the figure, on the pole where, tower is attached, the measure of side DC is 21.4 feet.
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;
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