Question

А A
ladder of 20m. high is
high is arranged
arranged stantly to
reach (touch the wall at a height of 10m
from its foot find the angle between

the ladder and ground and also the
distance between
the foot of ladder and
the
foot of the wall with process
​

Answer 1

Given:-

⠀⠀⠀◍ Length of ladder = 20m

⠀⠀⠀◍ Length of wall = 10m

⠀

To Find:-

⠀⠀⠀◍ Distance between the foot of

⠀⠀⠀⠀wall and foot of ladder.

⠀⠀⠀◍ Angle between the ladder

⠀⠀⠀⠀and ground

⠀

Let:-

⠀⠀⠀◍ Let ladder be = LA

⠀⠀⠀◍ Let wall be = AO

⠀⠀⠀◍ Let distance between their foot

⠀⠀⠀⠀= LO

⠀

Identity used:-

⠀⠀⠀◍ Sin Ø = $\dfrac{P}{H}$

⠀⠀⠀◍ Tan Ø = $\dfrac{P}{B}$

⠀⠀

⠀

Solution:-

★ Angle between the ladder and ground

⠀⠀⠀✯ Sin Ø = $\dfrac{P}{H}$

⠀⠀⠀✯ Sin Ø = $\dfrac{10}{20}$

⠀⠀⠀✯ Sin 30° = $\dfrac{1}{2}$

⠀⠀⠀✯ $\fbox{ Ø = 30°}$

⠀

★ Distance between their foot

⠀⠀⠀✯ Tan Ø = $\dfrac{P}{B}$

⠀⠀⠀✯ Tan 30° = $\dfrac{P}{B}$

⠀⠀⠀✯ $\dfrac{1}{√3}$ = $\dfrac{10}{LO}$

⠀⠀⠀✯ LO = 10√3

⠀⠀⠀✯ LO = 17.32

⠀

⠀

So,

⠀⠀⠀★ The angle between the ladder

⠀⠀⠀⠀and ground = 30°

⠀⠀⠀★ The distance between their foot

⠀⠀⠀⠀= 17.32