Question

A ladder of length 4m leans against a vertical wall so that the base of the ladder is 2m from the wall. Calculate the angle between the ladder and the wall?

Answer 1

Given:

A ladder of length 4m leans against a vertical wall so that the base of the ladder is 2m from the wall. Calculate the angle between the ladder and the wall?

To find:

The angle between the ladder and the wall?

Solution:

Considering the given situation in the form of a right-angled triangle ABC where we have:

"AB" = the height of the vertical wall

"BC" = the distance between the base of the ladder and the wall = 2 m

"AC" = the length of the ladder = 4 m

"∠CAB" = θ = the angle between the ladder and the wall

Here we will use the trigonometric ratio of a triangle

i.e., $\boxed{\bold{sin \:\theta = \frac{Perpendicular}{Hypotenuse} }}$

As per the question, we have

Perpendicular = BC = 2 m

Hypotenuse = AC = 4 m

θ = ∠CAB

∴ $sin \:\theta = \frac{BC}{AC}$

$\implies sin \:\theta = \frac{2}{4}$

$\implies sin \:\theta = \frac{1}{2}$

tanking sin inverse on both sides

$\implies sin^-^1(sin \:\theta)= sin^-^1(\frac{1}{2})$

$\implies \theta= sin^-^1(\frac{1}{2})$

$\implies \bold{\theta=30\°}$

Thus, the angle between the ladder and the vertical wall is → 30°.

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