Question : A ladder leaning against a wall makes an angle $\theta$ with the horizontal ground such that $\tan \theta=\frac{12}{5}$. If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the foot of the ladder from the wall?
Option 1: 18
Option 2: 19.5
Option 3: 7.5
Option 4: 10
Correct Answer: 10
Solution :
The ladder leaning against the wall makes an angle $\theta$ with the horizontal ground such that $\tan \theta = \frac{12}{5}$.
The height of the top of the ladder from the wall is = 24 m
Concept Used:
$\tan \theta = \frac{\text{Height}}{\text{Base}}$
Accordingly,
Let the base = x which means the distance of the foot of the ladder from the wall is x
$\tan \theta = \frac{12}{5}$
$⇒\frac{24}{\text{x}} = \frac{12}{5}$
$⇒\text{x} = 10$ m
$\therefore$ The distance of the foot of the ladder from the wall is 10 m.
Hence, the correct answer is 10 m.
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