Question

The heights of two poles are 80 m and 65 m. If the line joining their tops makes an angle of 45° 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

(a) 15 m
Let $AB$and $CD$ be the poles of heights of 80 m and 65 m, respectively.
Draw $DE$⊥ $AB$.
Now,
∠$EDB={45}^o$
Also,
$EB=AB-AE=AB-CD=80-65=15$ m

In ∆$BED$, we have:
$\frac{ED}{EB}=cot{45}^o=1$
⇒ $\frac{ED}{15}=1$
⇒ $ED=15$ m
∴ $AC=ED=15$ m

Hence, the distance between the poles is 15 m.