A ladder rests against a vertical wall at an inclination of 60 degrees to the horizontal Its foot is - Maths - Some Applications of Trigonometry

Question

A ladder rests against a vertical wall at an inclination of 60
degrees to the horizontal Its foot is pulled away from the wall
through a distance "p"m so that the upper end slides down a
distance of "q" m along the wall and then the ladder makes an angle
45 degrees to the horizontal Find the value of p/q

Abhishek Jha · Accepted Answer

Dear Student,
Here is the solution of your asked query:
The given information can be represented diagrammatically
as
<img alt="" height="143" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/27Janiv%20png"
width="178">
In the above figure AB and CD represent the same ladder
So, their length must be equal
Let length of the ladder be h
∴ AB = CD = h
Here, α=60° and β=45°In △AEB;AEAB=sinα=sin60°=32⇒AE=h32and BEAB=cosα=cos60°=12⇒BE=h2Now, In △DEC;DECD=sinβ=sin45°=12⇒DE=h2and CECD=cosβ=cos45°=12⇒CE=h2Now, pq=BCAD               =CE-BEAE-DE               =h2-h2h32-h2               =h2-h2h3-h22             =h2-hh3-h2 =2-13-2
Regards