4 Views

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


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books