The tower is 70 m high and and the wire is knoteed from the top of 20 m of the tower,
Here, AB represent the tower, AB = 70m
and AD represent the 20 m from the top, AD = 20m
SInce the wire is knotted from the top of 20m i.e. the wire is knotted at point D
Thus, BD = AB - AD
BD = 70 - 20
BD = 50m
The wire is knotted to the ground at point C;
and Angle C = 46°
Here, we need to find the length of the wire, i,e we need to find the length of side CD
In the diagram, CBD makes a right angle triangle,
Angle C = 46, and the side opposite to the angle C is BD = 50 and Hypotenuse CD
Apply the trigonometric ratio of Sine of angle 46
Since,
[tex]\sin \theta=\frac{Opposite\text{ side}}{Hypotenuse}[/tex]Substitute angle = 46, Opposite side BD = 50 and Hypotenuse CD
[tex]\begin{gathered} \sin \theta=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin 46=\frac{BD}{CD} \\ CD=\frac{BD}{\sin 46} \\ CD=\frac{50}{0.719} \\ CD=69.54\text{ m} \end{gathered}[/tex]Therefore, the length of the wire is 69.54 m
Answer: 69.5m
