Question

A cable tied to the top of an electric pole is affixed at a point on the ground $a\text{m}$ away from the pole. If the cable makes an angle $\theta$ with ground, then the height of the pole is _____.

• A. $a\sec \theta$
• B. $a\cos \theta$
• C. $a\sin \theta$
• D. $a\tan \theta$

Answer 1

The correct option is D $a\tan \theta$

Referring to the figure,

$AB=$ pole,

$AC=$ cable and

$BC=$ distance between pole and cable $=a$

It is clear that $\angle B={90}^o$, $\angle C=\theta$

$\therefore tan\theta =\frac{AB}{BC}=\frac{AB}{a}$

$\therefore AB=atan\theta$

$\therefore$ Height of the pole is $atan\theta$