Question

Two vertical poles are 40 meters apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Find their heights.​

Answer 1

Answer:

The heights of poles are $14.14$ and $28.28.$

Step-by-step explanation  

Given: Two vertical poles are $40$ meters apart and the height of one is double that of the other and the angles of elevation are complimentary.

To Find: The heights of poles.

Solution: Let $A B$ and $C D$ be the vertical poles such that the height of one is double to that of the other.

As is it given that the angular elevations of the poles tops are complementary.

So, assume that the angle made by smaller pole $=\theta.$

Therefore, the angle made by $D E$ is $90-\theta.$

In $\triangle A B C, \tan (\theta)=\frac{h}{20}$

and

In $\triangle C D E, \tan (\theta)=\frac{20}{2 h}$

By equating the values of $\text{tan} \;(\theta),$

$\frac{h}{20}=\frac{20}{2 h}$

$h^{2}=200$

$h=14.14$

Hence, the height of poles are $14.14$ and $28.28.$