Question

The heights of two poles are $80$ m and $65$ m. If the line joining their tops makes an angle of ${45}^{\circ }$ with the horizontal, then the distance between the poles is :

• A. $15$ m
• B. $22.5$ m
• C. $30$ m
• D. $7.5$ m

Answer 1

The correct option is A $15$ m

Let, $AB$ and $CD$ be the two poles of height $80$ m and $65$ m respectively.

According to the picture,

$AE=AB-CD=$$(80-65)m=15m$ [Since $CD=EB$]

Now, from $\Delta$ $ACE$ we have,

$\tan {45}^o=\frac{AE}{EC}$

$\Rightarrow 1=\frac{15}{EC}$

$\Rightarrow EC=15$

Now, $BD=EC=15m$.

Hence, the distance between the two poles is $15m$.