Question

The tops of two poles with height 25 m and 35 m are connected by a wire which is inclined to the horizontal at an angle of 30${}^0$. Find the length of the wire.

Answer 1

Given that, the tops of two poles with height $25m$ and $35m$ are connected by a wire which is inclined to the horizontal at an angle of ${30}^0$.

To find out: The length of the wire.

Based on the given information, we can draw the figure shown above.

$AE=25BD=BC+CD=35\therefore BC=35-25=10$

$In△ABC,\sin {30}^0=\frac{BC}{AB}=\frac{10}{AB}[\because \sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}]$

$AB=\frac{10}{\frac{1}{2}}[\because \sin {30}^0=\frac{1}{2}]$

$=20$

$\therefore$ Length of wire $\left(AB\right)=20m$

Hence, the length of the wire connecting the two poles is $20m$.