Question

Two towers are in front of each other, and their heights are 25 m and 10 m. The distance between them is 15 m.
What angle does the line joining their tops make with the ground?​

Answer 1

Given data:

Heights of two towers are $\mathsf{25}$ m and $\mathsf{10}$ m

Distance between them is $\mathsf{15}$ m

To find:

What angle does the line joining their tops make with the ground?

Step-by-step explanation:

First we draw the attached figure with some assumptions as follows,

$\mathsf{AB=25}$ m, $\mathsf{CD=10}$ m and $\mathsf{AC}$ is the line joining the tops of $\mathsf{AB}$ and $\mathsf{CD}$.

Since $\mathsf{CD=BE}$, then $\mathsf{BE=10}$ m

Then $\mathsf{AE=AB-BE=25-10}$ m $=15$ m

Since $\mathsf{BD=CE}$, then $\mathsf{CE=15}$ m

From $\mathsf{\Delta AEC}$, we get

$\quad \mathsf{tan(\angle ACE)=\dfrac{AE}{CE}}$

$\Rightarrow \mathsf{tan(\angle ACE)=\dfrac{15}{15}}$

$\Rightarrow \mathsf{tan(\angle ACE)=1=tan\dfrac{\pi}{4}}$

$\Rightarrow \mathsf{\angle ACE=\dfrac{\pi}{4}}$

Since $\mathsf{\Delta AEC}$ and $\mathsf{\Delta ABP}$ are similar triangles, $\mathsf{\angle ACE=\angle APB}$

$\Rightarrow \mathsf{\angle APB=\dfrac{\pi}{4}}$.

Answer:

The line joining the tops of the given towers makes an angle $\mathsf{\dfrac{\pi}{4}}$ with the ground.

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