Question : A ladder leaning against a wall makes an angle $\theta$ with the horizontal ground such that $\cos \theta=\frac{5}{13}$. If the height of the top of the ladder from the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall?
Option 1: 18
Option 2: 7.5
Option 3: 13
Option 4: 19.5
Correct Answer: 7.5
Solution :
Let's the distance of the foot of the ladder as $x$, and the height of the top of the ladder is 18 m
Length of the ladder = $L$ (Hypotenuse)
$h$ = 18 cm and cos θ = $\frac{5}{13}$
Now,
⇒ cos θ = $\frac{5}{13}$
So, tan θ = $\frac{\sqrt{(13^2-5^2)}}{5}= \frac{12}{5}$
⇒ $\frac{18}{x}= \frac{12}{5}$
⇒ $x$ = 7.5 m
Hence, the correct answer is 7.5.
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